16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.5.1

Inner Product Spaces

Mathematics — Linear Algebra · diagonalization-symmetric-matrices

Problem

For each of the following real symmetric matrices

A

, find a real orthogonal matrix

P

such that

P^tAP

is diagonal.

\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}, \quad \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}, \quad \begin{bmatrix} \cos\theta & \sin\theta \\ \sin\theta & -\cos\theta \end{bmatrix}