Linear map and Tensor

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Difference between Linear map and Tensor

Linear map vs. Tensor

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. In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

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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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Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

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Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

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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.

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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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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.

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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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General linear group

In mathematics, the general linear group of degree n is the set of invertible matrices, together with the operation of ordinary matrix multiplication.

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Linear form

In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.

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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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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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Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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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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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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