Are Linear Maps Finite Dimensional?

Given again the finite-dimensional case, if bases have been chosen, then the composition of linear maps corresponds to the matrix multiplication, the addition of linear maps corresponds to the matrix addition, and the multiplication of linear maps with scalars corresponds to the multiplication of matrices with scalars.

Is linear operator finite-dimensional?

If is a finite dimensional vector space, L: V → V is a linear operator having matrix A (with respect to some ordered basis for ), and A is diagonalizable, then the Diagonalization Method of Section 3.4 can be used to find the eigenvalues of L and a basis of fundamental eigenvectors for L. ■ Let be a finite dimensional ...

Are linear maps always continuous?

A linear map from a finite-dimensional space is always continuous.