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Needs:
Linear Transformations
Vector Space Dimensions
Needed by:
General Linear Groups
Links:
Sheet PDF
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Vector Space Isomorphisms

Why

In some sense, $\R ^n$ is the only finite-dimensional vector space. In what sense?

Definition

An isomorphism is an invertible linear transformation between two vector spaces. Two vector spaces are isomorphic if there exists and isomorphism between them.

Key result

Two finite-dimensional vector spaces are isomorphic if and only if they have the same dimension.
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