Question

Coefficient of characteristic polynomial as sum of principal minors

score 4.9k · Answer 1 · 2026-03-28 07:34:51

4.9k

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Coefficient of characteristic polynomial as sum of principal minors

Published on 28 Mar 2026 - 7:34

score 146 · Answer 2 · 2026-03-27 20:55:06

146

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Calculate the determinant of $A-2A^{-1}$ given the characteristic and minimal polynomials of $A$

Published on 27 Mar 2026 - 20:55

score 409 · Answer 3 · 2026-03-25 23:39:33

409

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Show that $\det(xA+yB+zI_{n})=\det(yA+xB+zI_{n})$

Published on 25 Mar 2026 - 23:39

score 111 · Answer 4 · 2026-05-10 21:36:09

111

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Show that $A+B=AB+BA$ iff $\text{Tr}(A)=\text{Tr}(B)=\text{Tr}(AB)=1$

Published on 10 May 2026 - 21:36

score 23 · Answer 5 · 2026-03-25 22:04:10

23

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Best (or correct) approach on finding characteristic polynomial of this $4 \times 4$ matrix

Published on 25 Mar 2026 - 22:04

score 66 · Answer 6 · 2026-03-25 22:09:13

66

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Characteristic polynomial of real matrix with complex eigenvalues

Published on 25 Mar 2026 - 22:09

score 94 · Answer 7 · 2026-03-25 23:36:55

94

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Show that there exists $A$ $(n×n)$ matrix with complex entries such that...

Published on 25 Mar 2026 - 23:36

score 136 · Answer 8 · 2026-03-26 01:12:17

136

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Show that $\operatorname{rank}(A)=\operatorname{rank}(A^{k})$ for every $k\geq1$ if and only if there exists $m\geq2$ such that $A^{m}=A$

Published on 26 Mar 2026 - 1:12

score 112 · Answer 9 · 2026-03-26 01:11:03

112

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The rank of the characteristic polynomial of a $\lambda$-matrix

Published on 26 Mar 2026 - 1:11

score 58 · Answer 10 · 2026-03-25 23:42:43

58

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Prove dimension of kernel of irreducible quadratic factor of characteristic polynomial is less then doubled multiplicity of respective complex root

Published on 25 Mar 2026 - 23:42

score 183 · Answer 11 · 2026-03-25 20:35:32

183

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What are the eigenvalues of this arrowhead matrix?

Published on 25 Mar 2026 - 20:35

score 78 · Answer 12 · 2026-03-25 23:42:21

78

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How to find ${\rm rank}(2I_n-A)$ where A is a square matrix of size $n$ and $A^3 - 6A^2 + 12A = 0_n$?

Published on 25 Mar 2026 - 23:42

score 66 · Answer 13 · 2026-03-25 23:40:28

66

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Proof that the characteristic polynomial of a matrix can be expressed as a sum of the matrix's determinant and scaled powers of its eigen values

Published on 25 Mar 2026 - 23:40

score 65 · Answer 14 · 2026-03-26 01:02:37

65

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Why is the following "proof" false?

Published on 26 Mar 2026 - 1:02

score 36 · Answer 15 · 2026-03-26 01:23:37

36

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$A ∈ GL_n(K)$. Show that there exists a polynomial $P(X) ∈ K[X]$ of degree $< n$ such that $A^{−1} = P(A)$

Published on 26 Mar 2026 - 1:23

List Question

Coefficient of characteristic polynomial as sum of principal minors

Calculate the determinant of $A-2A^{-1}$ given the characteristic and minimal polynomials of $A$

Show that $\det(xA+yB+zI_{n})=\det(yA+xB+zI_{n})$

Show that $A+B=AB+BA$ iff $\text{Tr}(A)=\text{Tr}(B)=\text{Tr}(AB)=1$

Best (or correct) approach on finding characteristic polynomial of this $4 \times 4$ matrix

Characteristic polynomial of real matrix with complex eigenvalues

Show that there exists $A$ $(n×n)$ matrix with complex entries such that...

Show that $\operatorname{rank}(A)=\operatorname{rank}(A^{k})$ for every $k\geq1$ if and only if there exists $m\geq2$ such that $A^{m}=A$

The rank of the characteristic polynomial of a $\lambda$-matrix

Prove dimension of kernel of irreducible quadratic factor of characteristic polynomial is less then doubled multiplicity of respective complex root

What are the eigenvalues of this arrowhead matrix?

How to find ${\rm rank}(2I_n-A)$ where A is a square matrix of size $n$ and $A^3 - 6A^2 + 12A = 0_n$?

Proof that the characteristic polynomial of a matrix can be expressed as a sum of the matrix's determinant and scaled powers of its eigen values

Why is the following "proof" false?

$A ∈ GL_n(K)$. Show that there exists a polynomial $P(X) ∈ K[X]$ of degree $< n$ such that $A^{−1} = P(A)$

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