Kronecker sum (source code)

= Kronecker sum
{title2=$A\oplus B=A\otimes I+I\otimes B$}

The <Kronecker sum> of square <matrices> combines their <Kronecker products> with <identity matrices>. If $Ax=\lambda x$ and $By=\mu y$, then $x\otimes y$ is an <eigenvector> with <eigenvalue> $\lambda+\mu$. Tensor-product spatial grids therefore turn separated coordinate Laplacians into a <Kronecker sum>. Two <Hermitian matrices> give a Hermitian <Kronecker sum>, allowing an <energy method> without computing every eigenvector.