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.