 Joint spectrum (source code)

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= Joint spectrum
{title2=$\operatorname{Spec}(A_1,\ldots,A_r)$}

For commuting diagonalizable operators $A_1,\ldots,A_r$ on a finite-dimensional <vector space>, the joint spectrum is the set of tuples $(a_1,\ldots,a_r)$ for which there is a common nonzero <eigenvector> $v$ with $A_iv=a_iv$. Commuting self-adjoint operators on a finite-dimensional <inner-product space> admit a simultaneous <orthonormal eigenbasis>.

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