Faster access than browser!
96 relations: Algebraic structure, Algorithm, Alphabetical order, Approximation, Arrangement of hyperplanes, Augmented matrix, Basis (linear algebra), Cartesian coordinate system, Chemistry, Cholesky decomposition, Coates graph, Coefficient matrix, Complex number, Complex system, Computer science, Computer simulation, Contradiction, Cracovian, Degrees of freedom (statistics), Determinant, Dimension, Dimension (vector space), Economics, Elementary algebra, Elementary matrix, Empty set, Engineering, Equation solving, Field (mathematics), Flat (geometry), Gaussian elimination, Gröbner basis, Hyperplane, Image (mathematics), Independent equation, Integer, Integer programming, Integral domain, Intersection (set theory), Invertible matrix, Iterative method, Iterative refinement, Kernel (linear algebra), LAPACK, Levinson recursion, Line (geometry), Linear algebra, Linear combination, Linear equation, Linear equation over a ring, ..., Linear independence, Linear least squares (mathematics), Linear map, Linear span, Linearization, LU decomposition, Mathematical model, Mathematics, Matrix (mathematics), Matrix decomposition, Matrix splitting, Module (mathematics), Moore–Penrose inverse, NAG Numerical Library, Nonlinear system, Numerical linear algebra, Overdetermined system, Parallel (geometry), Physics, Pivot element, Plane (geometry), Polynomial, Positive-definite matrix, Quantum algorithm for linear systems of equations, Rank (linear algebra), Rational number, Real number, Ring (mathematics), Rouché–Capelli theorem, Row and column vectors, Row echelon form, Scalar (mathematics), Set (mathematics), Solution set, Sparse matrix, Symmetric matrix, System of equations, Three-dimensional space, Toeplitz matrix, Translation (geometry), Tropical geometry, Underdetermined system, Variable (mathematics), Vector (mathematics and physics), Vector space, Zero element. Expand index (46 more) »
Algebraic structure
In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.
New!!: System of linear equations and Algebraic structure · See more »
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
New!!: System of linear equations and Algorithm · See more »
Alphabetical order
Alphabetical order is a system whereby strings of characters are placed in order based on the position of the characters in the conventional ordering of an alphabet.
New!!: System of linear equations and Alphabetical order · See more »
Approximation
An approximation is anything that is similar but not exactly equal to something else.
New!!: System of linear equations and Approximation · See more »
Arrangement of hyperplanes
In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space.
New!!: System of linear equations and Arrangement of hyperplanes · See more »
Augmented matrix
In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.
New!!: System of linear equations and Augmented matrix · See more »
Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
New!!: System of linear equations and Basis (linear algebra) · See more »
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
New!!: System of linear equations and Cartesian coordinate system · See more »
Chemistry
Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.
New!!: System of linear equations and Chemistry · See more »
Cholesky decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃ-/) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g. Monte Carlo simulations.
New!!: System of linear equations and Cholesky decomposition · See more »
Coates graph
In mathematics, the Coates graph or Coates flow graph, named after C.L. Coates, is a graph associated with the Coates' method for the solution of a system of linear equations.
New!!: System of linear equations and Coates graph · See more »
Coefficient matrix
In linear algebra, a coefficient matrix is a matrix consisting of the coefficients of the variables in a set of linear equations.
New!!: System of linear equations and Coefficient matrix · See more »
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
New!!: System of linear equations and Complex number · See more »
Complex system
A complex system is a system composed of many components which may interact with each other.
New!!: System of linear equations and Complex system · See more »
Computer science
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
New!!: System of linear equations and Computer science · See more »
Computer simulation
Computer simulation is the reproduction of the behavior of a system using a computer to simulate the outcomes of a mathematical model associated with said system.
New!!: System of linear equations and Computer simulation · See more »
Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions.
New!!: System of linear equations and Contradiction · See more »
Cracovian
In astronomical and geodetic calculations, Cracovians are a clerical convenience introduced in the 1930s by Tadeusz Banachiewicz for solving systems of linear equations by hand.
New!!: System of linear equations and Cracovian · See more »
Degrees of freedom (statistics)
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.
New!!: System of linear equations and Degrees of freedom (statistics) · See more »
Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
New!!: System of linear equations and Determinant · See more »
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
New!!: System of linear equations and Dimension · See more »
Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
New!!: System of linear equations and Dimension (vector space) · See more »
Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
New!!: System of linear equations and Economics · See more »
Elementary algebra
Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.
New!!: System of linear equations and Elementary algebra · See more »
Elementary matrix
In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation.
New!!: System of linear equations and Elementary matrix · See more »
Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
New!!: System of linear equations and Empty set · See more »
Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
New!!: System of linear equations and Engineering · See more »
Equation solving
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign.
New!!: System of linear equations and Equation solving · See more »
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
New!!: System of linear equations and Field (mathematics) · See more »
Flat (geometry)
In geometry, a flat is a subset of n-dimensional space that is congruent to a Euclidean space of lower dimension.
New!!: System of linear equations and Flat (geometry) · See more »
Gaussian elimination
In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
New!!: System of linear equations and Gaussian elimination · See more »
Gröbner basis
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field.
New!!: System of linear equations and Gröbner basis · See more »
Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
New!!: System of linear equations and Hyperplane · See more »
Image (mathematics)
In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.
New!!: System of linear equations and Image (mathematics) · See more »
Independent equation
An independent equation is an equation in a system of simultaneous equations which cannot be derived algebraically from the other equations.
New!!: System of linear equations and Independent equation · See more »
Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
New!!: System of linear equations and Integer · See more »
Integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
New!!: System of linear equations and Integer programming · See more »
Integral domain
In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.
New!!: System of linear equations and Integral domain · See more »
Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
New!!: System of linear equations and Intersection (set theory) · See more »
Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
New!!: System of linear equations and Invertible matrix · See more »
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
New!!: System of linear equations and Iterative method · See more »
Iterative refinement
Iterative refinement is an iterative method proposed by James H. Wilkinson to improve the accuracy of numerical solutions to systems of linear equations.
New!!: System of linear equations and Iterative refinement · See more »
Kernel (linear algebra)
In mathematics, and more specifically in linear algebra and functional analysis, the kernel (also known as null space or nullspace) of a linear map between two vector spaces V and W, is the set of all elements v of V for which, where 0 denotes the zero vector in W. That is, in set-builder notation,.
New!!: System of linear equations and Kernel (linear algebra) · See more »
LAPACK
LAPACK (Linear Algebra Package) is a standard software library for numerical linear algebra.
New!!: System of linear equations and LAPACK · See more »
Levinson recursion
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix.
New!!: System of linear equations and Levinson recursion · See more »
Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
New!!: System of linear equations and Line (geometry) · See more »
Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
New!!: System of linear equations and Linear algebra · See more »
Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
New!!: System of linear equations and Linear combination · See more »
Linear equation
In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.
New!!: System of linear equations and Linear equation · See more »
Linear equation over a ring
In algebra, linear equations and systems of linear equations over a field are widely studied.
New!!: System of linear equations and Linear equation over a ring · See more »
Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
New!!: System of linear equations and Linear independence · See more »
Linear least squares (mathematics)
In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model.
New!!: System of linear equations and Linear least squares (mathematics) · See more »
Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
New!!: System of linear equations and Linear map · See more »
Linear span
In linear algebra, the linear span (also called the linear hull or just span) of a set of vectors in a vector space is the intersection of all subspaces containing that set.
New!!: System of linear equations and Linear span · See more »
Linearization
In mathematics, linearization is finding the linear approximation to a function at a given point.
New!!: System of linear equations and Linearization · See more »
LU decomposition
In numerical analysis and linear algebra, LU decomposition (where "LU" stands for "lower–upper", and also called LU factorization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix.
New!!: System of linear equations and LU decomposition · See more »
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language.
New!!: System of linear equations and Mathematical model · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: System of linear equations and Mathematics · See more »
Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
New!!: System of linear equations and Matrix (mathematics) · See more »
Matrix decomposition
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices.
New!!: System of linear equations and Matrix decomposition · See more »
Matrix splitting
In the mathematical discipline of numerical linear algebra, a matrix splitting is an expression which represents a given matrix as a sum or difference of matrices.
New!!: System of linear equations and Matrix splitting · See more »
Module (mathematics)
In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.
New!!: System of linear equations and Module (mathematics) · See more »
Moore–Penrose inverse
In mathematics, and in particular linear algebra, a pseudoinverse of a matrix is a generalization of the inverse matrix.
New!!: System of linear equations and Moore–Penrose inverse · See more »
NAG Numerical Library
The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group.
New!!: System of linear equations and NAG Numerical Library · See more »
Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
New!!: System of linear equations and Nonlinear system · See more »
Numerical linear algebra
Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.
New!!: System of linear equations and Numerical linear algebra · See more »
Overdetermined system
In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.
New!!: System of linear equations and Overdetermined system · See more »
Parallel (geometry)
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.
New!!: System of linear equations and Parallel (geometry) · See more »
Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
New!!: System of linear equations and Physics · See more »
Pivot element
The pivot or pivot element is the element of a matrix, or an array, which is selected first by an algorithm (e.g. Gaussian elimination, simplex algorithm, etc.), to do certain calculations.
New!!: System of linear equations and Pivot element · See more »
Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
New!!: System of linear equations and Plane (geometry) · See more »
Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
New!!: System of linear equations and Polynomial · See more »
Positive-definite matrix
In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.
New!!: System of linear equations and Positive-definite matrix · See more »
Quantum algorithm for linear systems of equations
The quantum algorithm for linear systems of equations, designed by Aram Harrow, Avinatan Hassidim, and Seth Lloyd, is a quantum algorithm formulated in 2009 for solving linear systems.
New!!: System of linear equations and Quantum algorithm for linear systems of equations · See more »
Rank (linear algebra)
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.
New!!: System of linear equations and Rank (linear algebra) · See more »
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
New!!: System of linear equations and Rational number · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: System of linear equations and Real number · See more »
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
New!!: System of linear equations and Ring (mathematics) · See more »
Rouché–Capelli theorem
The Rouché–Capelli theorem is a theorem in linear algebra that allows computing the number of solutions in a system of linear equations given the rank of its augmented matrix and coefficient matrix.
New!!: System of linear equations and Rouché–Capelli theorem · See more »
Row and column vectors
In linear algebra, a column vector or column matrix is an m × 1 matrix, that is, a matrix consisting of a single column of m elements, Similarly, a row vector or row matrix is a 1 × m matrix, that is, a matrix consisting of a single row of m elements Throughout, boldface is used for the row and column vectors.
New!!: System of linear equations and Row and column vectors · See more »
Row echelon form
In linear algebra, a matrix is in echelon form if it has the shape resulting from a Gaussian elimination.
New!!: System of linear equations and Row echelon form · See more »
Scalar (mathematics)
A scalar is an element of a field which is used to define a vector space.
New!!: System of linear equations and Scalar (mathematics) · See more »
Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
New!!: System of linear equations and Set (mathematics) · See more »
Solution set
In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
New!!: System of linear equations and Solution set · See more »
Sparse matrix
In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero.
New!!: System of linear equations and Sparse matrix · See more »
Symmetric matrix
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.
New!!: System of linear equations and Symmetric matrix · See more »
System of equations
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
New!!: System of linear equations and System of equations · See more »
Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
New!!: System of linear equations and Three-dimensional space · See more »
Toeplitz matrix
In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant.
New!!: System of linear equations and Toeplitz matrix · See more »
Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.
New!!: System of linear equations and Translation (geometry) · See more »
Tropical geometry
Tropical geometry is a relatively new area in mathematics, which might loosely be described as a piece-wise linear or skeletonized version of algebraic geometry.
New!!: System of linear equations and Tropical geometry · See more »
Underdetermined system
In mathematics, a system of linear equations or a system of polynomial equations is considered underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns).
New!!: System of linear equations and Underdetermined system · See more »
Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
New!!: System of linear equations and Variable (mathematics) · See more »
Vector (mathematics and physics)
When used without any further description, vector usually refers either to.
New!!: System of linear equations and Vector (mathematics and physics) · See more »
Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
New!!: System of linear equations and Vector space · See more »
Zero element
In mathematics, a zero element is one of several generalizations of the number zero to other algebraic structures.
New!!: System of linear equations and Zero element · See more »
Redirects here:
Algorithms for solving systems of linear equations, Ax=0, Ax=b, Homogeneous equation, Homogeneous linear equation, Homogeneous system, Linear Equation System, Linear equation system, Linear simultaneous equations, Linear system of equations, Methods for solving systems of linear equations, Simultaneous linear equations, Solving systems of linear equations, Systems of linear equations, Vector equation.
References
[1] https://en.wikipedia.org/wiki/System_of_linear_equations
