16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.5.1

Elementary Canonical Forms

Mathematics — Linear Algebra · simultaneous-diagonalization

Problem

Find an invertible real matrix

P

such that

P^{-1}AP

and

P^{-1}BP

are both diagonal, where

A

and

B

are the real matrices (a)

A = \begin{bmatrix} 1 & 2 \\ 0 & 2 \end{bmatrix}, \qquad B = \begin{bmatrix} 3 & -8 \\ 0 & -1 \end{bmatrix}

(b)

A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}, \qquad B = \begin{bmatrix} 1 & a \\ a & 1 \end{bmatrix}.