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1 vote
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Is Rellich's function valued theorem valid for a rank defficient function valued matrix?

(ii) There exists an eigenvector $v_j(t)$ associated with $\lambda_j(t)$ for $j = 1,\cdots,n$ satisfying (1) $(\lambda_j(t)\boldsymbol{I} - \boldsymbol{A}(t))v_j(t)=0\forall t\in\mathbb{R}$ (2) $||v_j …
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1 answer
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The influence of eigendecomposition on the periodicity of a (rank 2) Hermitian matrix (of fu...

If $\boldsymbol{G}(u,v)=\lambda(u,v)\mathbf{x}(u,v)\mathbf{x}^{H}(u,v)$, where $\lambda(u,v)$ is the largest eigenvalue of $\boldsymbol{R}(u,v)$, $\mathbf{x}(u,v)$ is its associated eigenvector (normalized …
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