**Some Main Useful Theorems**

- A matrix is invertible, or non-singular, if and only if the linear map represented by the matrix is an isomorphism.
- Any vector space over a field
**F**of dimension*n*is isomorphic to**F***n*as a vector space over**F**. - Corollary: Any two vector spaces over
**F**of the same finite dimension are isomorphic to each other. - A linear map is an isomorphism if and only if the determinant is nonzero.

Read more about this topic: Linear Algebra

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