List questions from eigenvalues-eigenvectors

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Let $A$ be a $5 \times 5$ matrix in $\mathbb R.$ If $A^3=0$ and $\dim(\ker(A))+\dim(\ker(A^{2})=8$. Find the Jordan canonical form of $A.$

Published on 13 Apr 2026 - 6:43

2.2k

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Eigenvalues of the Schur complement

Published on 11 Apr 2026 - 0:56

174

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Perpendicular eigenvectors and symmetry

Published on 14 Apr 2026 - 6:19

513

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Prove that all the eigenvalues of $A$ are real.(Gershgorin 's Theorem)

Published on 23 Apr 2026 - 1:28

129

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Can I assign the term "is eigenvector" and "is eigenmatrix" of matrix P in my specific (infinite-size) case?

Published on 02 Dec 2019 - 12:41

97

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Matrix A with real eigenvalues such that $A^2$ is similar to $A$

Published on 11 Apr 2026 - 17:06

154

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Singular values vs eigenvalues for positive definite.

Published on 27 Mar 2026 - 3:56

350

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Prove: An × matrix has at most distinct eigenvalues (Using linear independence of eigenvectors)

Published on 14 Apr 2026 - 19:03

187

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Minimal polynomials and interpolation of eigenvalues

Published on 03 Dec 2019 - 15:07

164

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Eigenvalues Functional Analysis...

Published on 08 Apr 2026 - 12:43

302

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Eigenvalues of the hyperbolic Laplacian

Published on 11 Apr 2026 - 14:36

39

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Confusion regarding injectiveness of operator

Published on 08 Apr 2026 - 15:35

80

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eigenvectors of $A^2$ and $A$ if $A$ is positive definite.

Published on 27 Mar 2026 - 3:59

60

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Endomorphism of $S_n(\mathbf{R})$ such that $L(O^T S O) = O^T L(S) O$

Published on 25 Mar 2026 - 5:07

571

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Second Hadamard Variation Formula

Published on 11 Apr 2026 - 22:40

List Question

Let $A$ be a $5 \times 5$ matrix in $\mathbb R.$ If $A^3=0$ and $\dim(\ker(A))+\dim(\ker(A^{2})=8$. Find the Jordan canonical form of $A.$

Eigenvalues of the Schur complement

Perpendicular eigenvectors and symmetry

Prove that all the eigenvalues of $A$ are real.(Gershgorin 's Theorem)

Can I assign the term "is eigenvector" and "is eigenmatrix" of matrix P in my specific (infinite-size) case?

Matrix A with real eigenvalues such that $A^2$ is similar to $A$

Singular values vs eigenvalues for positive definite.

Prove: An × matrix has at most distinct eigenvalues (Using linear independence of eigenvectors)

Minimal polynomials and interpolation of eigenvalues

Eigenvalues Functional Analysis...

Eigenvalues of the hyperbolic Laplacian

Confusion regarding injectiveness of operator

eigenvectors of $A^2$ and $A$ if $A$ is positive definite.

Endomorphism of $S_n(\mathbf{R})$ such that $L(O^T S O) = O^T L(S) O$

Second Hadamard Variation Formula

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