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Eigen value minimization-Proof
The two minimization problems below are equivalent:
$\min\{\mathrm{trace}(AX^TBX): XX^T=I_n\}=\min\{\mathrm{trace}(AQ^T\tilde{B}Q): QQ^T=I_m\}$, where $A,\tilde{B}$ and $Q$ are square matrices of ...
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vote
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Is this a valid proof of eigenvectors/values of nonzeroilty?
Let $A$ be a square real matrix such that it is symmetric, show that if $Ax = \lambda x$ for some nonzero vector in $\mathbb{C}^n$, then in fact, $\operatorname{Re}(x)$ is an eigenvector of $A$ if it ...
