Question

The computation of power of a matrix becomes faster if it is diagonalizable.

(a) True

(b) False

The question was posed to me in class test.

I'd like to ask this question from Diagonalization Powers of a Matrix in section Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

Right option is (a) True

To explain I would say: Some of the applications of diagonalization of a matrix are:

The powers of a diagonalized matrix can be computed easily since the result is nothing but the powers of the diagonal elements obtained by diagonalization.

Reducing quadratic forms to canonical forms by orthogonal transformations.

In mechanics, it can be used to find the natural frequency of vibrations.