List questions from eigenvalues-eigenvectors

115

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Write $m_{I-A}$ (the minimal polynomial of $I-A$) in terms of $m_A$ and conclude: $\deg(m_A)=\deg(m_{I-A})$

Published on 22 Mar 2026 - 18:31

196

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Uniqueness of Eigenspaces

Published on 11 May 2018 - 20:14

12.6k

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Do Real Symmetric Matrices have 'n' linearly independent eigenvectors?

Published on 25 Mar 2026 - 19:03

165

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$T^m(v)=v$ implies $T$ diagonalizable

Published on 12 May 2018 - 4:24

151

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Shifting eigenvalues via skew-symmetric product

Published on 12 May 2018 - 4:43

21.2k

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How to find complex eigenvectors from complex eigenvalues?

Published on 12 May 2018 - 11:13

137

Views

Eigenvalues of linear operator of the space $\mathbb{R}[x,y]$

Published on 25 Mar 2026 - 3:20

56

Views

Surface described by ${\bf r^\top A r + b^\top r}=1$?

Published on 24 Mar 2026 - 22:09

92

Views

Order of eigenvectors sometimes important?

Published on 25 Mar 2026 - 4:55

102

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Generalized $\lambda$-eigenspace

Published on 25 Mar 2026 - 4:53

9.8k

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If $\lambda$ is an eigen value of an orthogonal matrix $A$, then show that $\frac{1}{\lambda}$ is also an eigen value of $A$

Published on 25 Mar 2026 - 17:40

144

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What is the quickest way to find whether the eigenvalues of a $2 \times 2$ matrix are inside the unit circle?

Published on 13 May 2018 - 11:09

3.1k

Views

When should we not use Gaussian elimination to find Eigen vectors?

Published on 25 Mar 2026 - 6:11

277

Views

Representing antisymmetric matrix in block diagonal form?

Published on 25 Mar 2026 - 23:36

600

Views

Existence of the maximum in the minimax principle of Courant-Fischer

Published on 26 Mar 2026 - 8:02

List Question

Write $m_{I-A}$ (the minimal polynomial of $I-A$) in terms of $m_A$ and conclude: $\deg(m_A)=\deg(m_{I-A})$

Uniqueness of Eigenspaces

Do Real Symmetric Matrices have 'n' linearly independent eigenvectors?

$T^m(v)=v$ implies $T$ diagonalizable

Shifting eigenvalues via skew-symmetric product

How to find complex eigenvectors from complex eigenvalues?

Eigenvalues of linear operator of the space $\mathbb{R}[x,y]$

Surface described by ${\bf r^\top A r + b^\top r}=1$?

Order of eigenvectors sometimes important?

Generalized $\lambda$-eigenspace

If $\lambda$ is an eigen value of an orthogonal matrix $A$, then show that $\frac{1}{\lambda}$ is also an eigen value of $A$

What is the quickest way to find whether the eigenvalues of a $2 \times 2$ matrix are inside the unit circle?

When should we not use Gaussian elimination to find Eigen vectors?

Representing antisymmetric matrix in block diagonal form?

Existence of the maximum in the minimax principle of Courant-Fischer

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