= Product Laplacian eigenspace decomposition
{title2=$E_\lambda(M\times N)=\bigoplus_{\mu+\nu=\lambda}E_\mu(M)\otimes E_\nu(N)$}
For <closed manifolds> with the product <Riemannian metric>, the <positive Laplace-Beltrami operator> is the sum of the two factor operators. Products of their <orthonormal eigenbases> form a complete basis, and <eigenvalues> add. Hence the product <eigenspace> at $\lambda$ is the displayed finite orthogonal sum of <tensor products>. The discrete assertion requires a discrete spectral setting.
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