Kunze Linear Algebra · Problem 8.5.3

Inner Product Spaces

Mathematics — Methods · diagonalizing-real-symmetric-matrices

Problem

For

A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{bmatrix}

there is a real orthogonal matrix

P

such that

P^tAP = D

is diagonal. Find such a diagonal matrix

D