Linear Algebra - Some Main Useful Theorems

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 Fn 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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