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

Famous quotes containing the word main:

    I do not deny that there may be other well-founded causes for the hatred which various classes feel toward politicians, but the main one seems to me that politicians are symbols of the fact that every class must take every other class into account.
    José Ortega Y Gasset (1883–1955)