Orthogonal Diagonalization

$$A = Q D Q^T$$

A square matrix $A$ is orthogonally diagonalizable if there exists an orthogonal matrix $Q$ and a diagonal matrix $D$ such that $Q^T A Q = D$. Any $n \times n$ real matrix is diagonalizable if and only if it is symmetric (the Spectral Theorem).

$D$ is a diagonal matrix built from $A$'s eigenvalues.

$Q$ is an orthogonal matrix derived from $A$'s eigenvectors. For any symmetric matrix, which $A$ is, any two of its eigenvectors corresponding to distinct eigenvalues are orthogonal. If we then normalize these eigenvectors we obtain $Q$.