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# Vector space/Related Articles

From Citizendium

*See also changes related to Vector space, or pages that link to Vector space or to this page or whose text contains "Vector space".*

## Parent topics

- Linear algebra [r]: Branch of mathematics that deals with the theory of systems of linear equations, matrices, vector spaces, determinants, and linear transformations.
^{[e]} - Vector [r]:
*Please do not use this term in your topic list, because there is no single article for it. Please substitute a more precise term. See vector (disambiguation) for a list of available, more precise, topics. Please add a new usage if needed.* - Scalar [r]: Real or complex number, or an invariant under orthogonal/unitary transformation of reference frame.
^{[e]}

- Abstract algebra [r]: Branch of mathematics that studies structures such as groups, rings, and fields.
^{[e]} - Module (mathematics) [r]:
*Add brief definition or description* - Space (mathematics) [r]: A set with some added structure, which often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space.
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## Subtopics

- Linear combination [r]: Expression of first order, composed of the sums and differences of elements with coefficients in a field, such as the field of real numbers.
^{[e]} - Linear independence [r]: The property of a system of elements of a module or vector space, that no non-trivial linear combination is zero.
^{[e]} - Span (algebra) [r]:
*Add brief definition or description* - Basis (linear algebra) [r]: A set of vectors that, in a linear combination, can represent every vector in a given vector space or free module, and such that no element of the set can be represented as a linear combination of the others.
^{[e]} - Dimension (vector space) [r]: The number of elements in any basis for a vector space.
^{[e]}

- Linear transformation [r]:
*Add brief definition or description* - Matrix representation [r]:
*Add brief definition or description* - Linear representation [r]:
*Add brief definition or description*

- Normed linear space [r]:
*Add brief definition or description* - Inner product space [r]: A vector space that is endowed with an inner product and the corresponding norm.
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