Spectral matrix functional calculus
= Spectral matrix functional calculus
{title2=$f(A)$}
For a <Hermitian matrix> with unitary diagonalization $A=U\operatorname{diag}(\lambda_i)U^*$, define $f(A)=U\operatorname{diag}(f(\lambda_i))U^*$ for a function on its finite spectrum. This acts on <eigenvalues>, unlike an <entrywise matrix function> $f[A]$. For example, the spectral square of a <matrix> is its ordinary <matrix> product with itself, whereas its entrywise square is a <Hadamard power>.