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: Super Linear Algebra
Famous quotes containing the word main:
“I could live without acting.... Acting is a gift I’ve received. And I’m grateful for it and I enjoy it. But it’s not the main point of my life. It never was.”
—Jeanne Moreau (b. 1928)