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Why does eigendecomposition is in the same form of $A=CBC^{-1}$ as using eigenvectors as basis for a transition matrix?

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#linear-algebra #eigenvalues-eigenvectors #change-of-basis
356
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If $\lambda$ is an eigenvalue for a linear operator $T(x)$ and if $g(t)$ is a polynomial, then $g(T(x)) = g(\lambda)x$

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#linear-algebra #polynomials #eigenvalues-eigenvectors
54
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Help to calculate eigenvectors

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#matrices #eigenvalues-eigenvectors
144
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trace of exterior product of a skew matrix $M$, $\bigwedge^kM$

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#linear-algebra #eigenvalues-eigenvectors #exterior-algebra
481
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Change order of eigenvalues and correspoding eigenvector

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#eigenvalues-eigenvectors #covariance
1.2k
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How the principal submatrix of a PSD matrix could be positive definite?

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#linear-algebra #matrices #eigenvalues-eigenvectors #positive-definite #positive-semidefinite
21.2k
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Why can the determinant be assumed to be 0?

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#linear-algebra #statistics #eigenvalues-eigenvectors #determinant
94
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Aribtrary large ratio for eigenvalues of positive definite matrices

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#linear-algebra #inequality #eigenvalues-eigenvectors #positive-definite
204
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Showing a block matrix is SPD

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#matrices #eigenvalues-eigenvectors #symmetric-matrices #positive-definite #block-matrices
100
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Is T diagonalizable for $V=\mathbb{R^2}$ ? For $V=\mathbb{C^2}$

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#linear-algebra #eigenvalues-eigenvectors #diagonalization
131
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Unusual normalization related to the eigenvector perturbation

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#matrices #eigenvalues-eigenvectors #matrix-calculus #perturbation-theory
434
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what does mean a zero eigenvalue in a PDE?

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#partial-differential-equations #numerical-methods #eigenvalues-eigenvectors #hyperbolic-equations
889
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Diagonally dominant matrix by rows and/or by columns

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#linear-algebra #graph-theory #eigenvalues-eigenvectors #spectral-graph-theory
41
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Why the restriction that no pole be on $\partial\Omega$?

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#real-analysis #partial-differential-equations #eigenvalues-eigenvectors
76
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Matrix and eigenvalue question

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#linear-algebra #matrices #eigenvalues-eigenvectors

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