Dimension theorem for vector spaces
id:
dimension-theorem-for-vector-spaces-264-5933921
title:
Dimension theorem for vector spaces
text:
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite or infinite, and defines the dimension of the vector space. Formally, the dimension theorem for vector spaces states that: As a basis is a generating set that is linearly independent, the dimension theorem is a consequence of the following theorem, which is also useful: In particular if V is finitely generated, then all its bases are fi
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wiki
category slug:
encyclopedia
description:
All bases of a vector space have equally many elements
original url:
https://en.wikipedia.org/wiki/Dimension_theorem_for_vector_spaces
date created:
date modified:
2024-02-08T22:18:42Z
main entity:
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13
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