Faster access than browser!
37 relations: Algebraic geometry, Basis (linear algebra), Canonical units, Cartesian coordinate system, Circumflex, Coordinate system, Dimension (vector space), Euclidean space, Field (mathematics), Free module, Grassmannian, Gröbner basis, Kronecker delta, Lie algebra, Linear combination, Mathematical notation, Mathematics, Matrix (mathematics), Monomial, Monomial basis, Orthogonality, Orthonormal basis, Physics, Poincaré–Birkhoff–Witt theorem, Polynomial, Representation theory, Ring (mathematics), Scalar (mathematics), Sequence, Three-dimensional space, Two-dimensional space, Unit vector, Universal enveloping algebra, Vector projection, Vector space, Versor (physics), W. V. D. Hodge.
Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
New!!: Standard basis and Algebraic geometry · 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!!: Standard basis and Basis (linear algebra) · See more »
Canonical units
A canonical unit is a unit of measurement agreed upon as default in a certain context.
New!!: Standard basis and Canonical units · 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!!: Standard basis and Cartesian coordinate system · See more »
Circumflex
The circumflex is a diacritic in the Latin, Greek and Cyrillic scripts that is used in the written forms of many languages and in various romanization and transcription schemes.
New!!: Standard basis and Circumflex · See more »
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
New!!: Standard basis and Coordinate system · 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!!: Standard basis and Dimension (vector space) · See more »
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
New!!: Standard basis and Euclidean space · 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!!: Standard basis and Field (mathematics) · See more »
Free module
In mathematics, a free module is a module that has a basis – that is, a generating set consisting of linearly independent elements.
New!!: Standard basis and Free module · See more »
Grassmannian
In mathematics, the Grassmannian is a space which parametrizes all -dimensional linear subspaces of the n-dimensional vector space.
New!!: Standard basis and Grassmannian · 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!!: Standard basis and Gröbner basis · See more »
Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
New!!: Standard basis and Kronecker delta · See more »
Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
New!!: Standard basis and Lie 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!!: Standard basis and Linear combination · See more »
Mathematical notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas.
New!!: Standard basis and Mathematical notation · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Standard basis 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!!: Standard basis and Matrix (mathematics) · See more »
Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
New!!: Standard basis and Monomial · See more »
Monomial basis
In mathematics the monomial basis of a polynomial ring is its basis (as vector space or free module over the field or ring of coefficients) that consists in the set of all monomials.
New!!: Standard basis and Monomial basis · See more »
Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
New!!: Standard basis and Orthogonality · See more »
Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
New!!: Standard basis and Orthonormal basis · 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!!: Standard basis and Physics · See more »
Poincaré–Birkhoff–Witt theorem
In mathematics, more specifically in abstract algebra, in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a Lie algebra.
New!!: Standard basis and Poincaré–Birkhoff–Witt theorem · 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!!: Standard basis and Polynomial · See more »
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
New!!: Standard basis and Representation theory · See more »
Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
New!!: Standard basis and Ring (mathematics) · See more »
Scalar (mathematics)
A scalar is an element of a field which is used to define a vector space.
New!!: Standard basis and Scalar (mathematics) · See more »
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
New!!: Standard basis and Sequence · 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!!: Standard basis and Three-dimensional space · See more »
Two-dimensional space
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
New!!: Standard basis and Two-dimensional space · See more »
Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
New!!: Standard basis and Unit vector · See more »
Universal enveloping algebra
In mathematics, a universal enveloping algebra is the most general (unital, associative) algebra that contains all representations of a Lie algebra.
New!!: Standard basis and Universal enveloping algebra · See more »
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.
New!!: Standard basis and Vector projection · 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!!: Standard basis and Vector space · See more »
Versor (physics)
In geometry and physics, the versor of an axis or of a vector is a unit vector indicating its direction.
New!!: Standard basis and Versor (physics) · See more »
W. V. D. Hodge
Sir William Vallance Douglas Hodge FRS FRSE (17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer.
New!!: Standard basis and W. V. D. Hodge · See more »
Redirects here:
Kronecker basis, Standard bases, Standard basis vector.
References
[1] https://en.wikipedia.org/wiki/Standard_basis
