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51 relations: Antilinear map, Banach space, Basis (linear algebra), Bilinear form, Bra–ket notation, Continuous function, Covariance and contravariance of vectors, Discontinuous linear map, Distribution (mathematics), Dot product, Dual basis, Dual space, Euclidean space, Euclidean vector, Field (mathematics), Function space, Functional analysis, General relativity, Generalized function, Gravitation (book), Hilbert space, Hodge star operator, Hyperplane, Inner product space, Integral, Isomorphism, Kernel (linear algebra), Kronecker delta, Lagrange polynomial, Level set, Levi-Civita symbol, Linear algebra, Linear combination, Linear map, Linear subspace, Matrix multiplication, Multilinear form, Norm (mathematics), Numerical integration, One-form, Orthogonality, Pointwise, Positive linear functional, Quantum mechanics, Riemann integral, Riesz representation theorem, Row and column vectors, Scalar (mathematics), Surjective function, Topological vector space, ..., Vector space. Expand index (1 more) »
Antilinear map
In mathematics, a mapping f:V\to W from a complex vector space to another is said to be antilinear (or conjugate-linear) if for all a, \, b \, \in \mathbb and all x, \, y \, \in V, where \bar and \bar are the complex conjugates of a and b respectively.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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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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Bilinear form
In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.
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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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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Covariance and contravariance of vectors
In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.
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Discontinuous linear map
In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as approximations to more general functions (see linear approximation).
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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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 basis
In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimensionality of V), its dual set is a set B∗ of vectors in the dual space V∗ with the same index set I such that B and B∗ form a biorthogonal system.
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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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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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Function space
In mathematics, a function space is a set of functions between two fixed sets.
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Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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Generalized function
In mathematics, generalized functions, or distributions, are objects extending the notion of functions.
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Gravitation (book)
Gravitation is a physics book on Einstein's theory of gravity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler and originally published by W. H. Freeman and Company in 1973.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Hodge star operator
In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.
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Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
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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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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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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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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,.
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Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
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Lagrange polynomial
In numerical analysis, Lagrange polynomials are used for polynomial interpolation.
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Level set
In mathematics, a level set of a real-valued function ''f'' of ''n'' real variables is a set of the form that is, a set where the function takes on a given constant value c. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline.
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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 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.
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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).
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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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Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
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Matrix multiplication
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.
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Multilinear form
In abstract algebra and multilinear algebra, a multilinear form on V is a map of the type f: V^k \to K,where V is a vector space over the field K (or more generally, a module over a commutative ring), that is separately K-linear in each of its k arguments.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.
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One-form
In linear algebra, a one-form on a vector space is the same as a linear functional on the space.
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Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
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Pointwise
In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function f. An important class of pointwise concepts are the pointwise operations — operations defined on functions by applying the operations to function values separately for each point in the domain of definition.
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Positive linear functional
In mathematics, more specifically in functional analysis, a positive linear functional on an ordered vector space (V, ≤) is a linear functional f on V so that for all positive elements v of V, that is v≥0, it holds that In other words, a positive linear functional is guaranteed to take nonnegative values for positive elements.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Riemann integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.
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Riesz representation theorem
There are several well-known theorems in functional analysis known as the Riesz representation theorem.
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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 (mathematics)
A scalar is an element of a field which is used to define a vector space.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
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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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Continuous linear functional, Covector, Dual vector, Linear forms, Linear functional, Linear functionals.
References
[1] https://en.wikipedia.org/wiki/Linear_form
