Linear Algebra properties

3D Inverse is unique

An invertible linear map has a unique inverse

3D Invertibility is equivalent to injectivity and surjectivity

A linear map is invertible IFF it is injective and surjective

3D Dimension shows whether vector spaces are isomorphic

Two finite dimensional vector space over F are isomorphic IFF they have the same dimensions

3D L(V, W) and F^(m, n) are isomorphic

Suppose v_1, …, v_n is a basis of V and w_1, …, w_m is a basis of W. Then M is an isomorphism between L(V, W) and F^(m,n)

3D dim L(V, W) = (dimV)(dimW)

If V and W are finite dimensional, then L(V, W) is finite dimensional.