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62 relations: Adjugate matrix, Associative property, Basis (linear algebra), Bra–ket notation, Cartesian coordinate system, Commutative property, Continuum mechanics, Cross product, Determinant, Differential form, Dimension, Distributive property, Dot product, Dual space, Electromagnetism, Engineering, Euclidean space, Euclidean vector, Field (mathematics), Inner product space, Isomorphism, Josiah Willard Gibbs, Kronecker product, Levi-Civita symbol, Linear map, Linearity, Lorentz factor, Lorentz transformation, Mathematics, Matrix (mathematics), Matrix ring, McGraw-Hill Education, Monomial, Multilinear algebra, Multiplicative inverse, Multivector, Outer product, Physics, Plane (geometry), Polyadic algebra, Pseudovector, Quaternion, Rank (linear algebra), Rodrigues' rotation formula, Rotation (mathematics), Row and column vectors, Scalar (physics), Scalar multiplication, Special relativity, Square matrix, ..., Standard basis, Stanford University, Tensor, Tensor (intrinsic definition), Tensor product, Three-dimensional space, Trace (linear algebra), Transpose, Unit vector, Vector algebra, Vector projection, Vector space. Expand index (12 more) »
Adjugate matrix
In linear algebra, the adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.
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Associative property
In mathematics, the associative property is a property of some binary operations.
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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.
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Bra–ket notation
In quantum mechanics, bra–ket notation is a standard notation for describing quantum states.
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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.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
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Cross product
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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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.
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Distributive property
In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
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Electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
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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.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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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.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
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Josiah Willard Gibbs
Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics.
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Kronecker product
In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.
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Levi-Civita symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.
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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.
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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Lorentz factor
The Lorentz factor or Lorentz term is the factor by which time, length, and relativistic mass change for an object while that object is moving.
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Lorentz transformation
In physics, the Lorentz transformations (or transformation) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix ring
In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication.
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McGraw-Hill Education
McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.
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Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
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Multilinear algebra
In mathematics, multilinear algebra extends the methods of linear algebra.
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Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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Multivector
A multivector is the result of a product defined for elements in a vector space V. A vector space with a linear product operation between elements of the space is called an algebra; examples are matrix algebra and vector algebra.
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Outer product
In linear algebra, an outer product is the tensor product of two coordinate vectors, a special case of the Kronecker product of matrices.
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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.
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Polyadic algebra
Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos.
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Pseudovector
In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but in three dimensions gains an additional sign flip under an improper rotation such as a reflection.
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Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers.
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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.
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Rodrigues' rotation formula
In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation.
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Rotation (mathematics)
Rotation in mathematics is a concept originating in geometry.
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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.
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Scalar (physics)
A scalar or scalar quantity in physics is a physical quantity that can be described by a single element of a number field such as a real number, often accompanied by units of measurement.
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Scalar multiplication
In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
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Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
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Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
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Standard basis
In mathematics, the standard basis (also called natural basis) for a Euclidean space is the set of unit vectors pointing in the direction of the axes of a Cartesian coordinate system.
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Stanford University
Stanford University (officially Leland Stanford Junior University, colloquially the Farm) is a private research university in Stanford, California.
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Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
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Tensor (intrinsic definition)
In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multi-linear concept.
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Tensor product
In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.
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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).
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Trace (linear algebra)
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.
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Transpose
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).
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Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
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Vector algebra
In mathematics, vector algebra may mean.
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Vector projection
The vector projection of a vector a on (or onto) a nonzero vector b (also known as the vector component or vector resolution of a in the direction of b) is the orthogonal projection of a onto a straight line parallel to b. It is a vector parallel to b, defined as where a_1 is a scalar, called the scalar projection of a onto b, and b̂ is the unit vector in the direction of b. In turn, the scalar projection is defined as where the operator · denotes a dot product, |a| is the length of a, and θ is the angle between a and b. The scalar projection is equal to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b. The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b, is the orthogonal projection of a onto the plane (or, in general, hyperplane) orthogonal to b. Both the projection a1 and rejection a2 of a vector a are vectors, and their sum is equal to a, which implies that the rejection is given by.
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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.
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Redirects here:
Diadic, Diadic product, Double-dot product, Dyad product, Dyadic product, Dyadic tensor.
References
[1] https://en.wikipedia.org/wiki/Dyadics
