Question

Any smart approach to finding a matrix given the characteristic polynomial?

score 257 · Answer 1 · 2026-03-25 09:25:36

257

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Any smart approach to finding a matrix given the characteristic polynomial?

Published on 25 Mar 2026 - 9:25

score 123 · Answer 2 · 2026-03-25 09:29:16

123

Views

Find all $n$ for which there exist A, B, matrices of size n with real entries, such that $A^2B-BA^2=A$.

Published on 25 Mar 2026 - 9:29

score 88 · Answer 3 · 2026-03-25 09:28:56

88

Views

If $A^3+2A^2+2A+I_n=0_n$, then $\det(A)=-1$, where $A$ is a square matrix of odd size, with real entries

Published on 25 Mar 2026 - 9:28

score 84 · Answer 4 · 2026-03-25 09:27:15

84

Views

How to find the matrix of an endomorphism in a cyclic basis?

Published on 25 Mar 2026 - 9:27

score 175 · Answer 5 · 2026-03-25 09:29:55

175

Views

There is a polynomial $g(x)\in\mathbb{R}[x_1,..., x_n]$ such that $f(X) = g(a_0,..., a_{n−1})$ where $a_i$ is the coefficient of $λ^i$

Published on 25 Mar 2026 - 9:29

score 85 · Answer 6 · 2026-04-01 10:15:32

85

Views

Eigenvalues of a certain block matrix

Published on 01 Apr 2026 - 10:15

score 31 · Answer 7 · 2026-03-25 09:29:51

31

Views

Show that $p_\rho(λ) = p_{\rho_1}(λ)p_{\rho_2}(λ)$ where $p_\rho,p_{\rho_1},p_{\rho_2}$ are the characteristic polynomials.

Published on 25 Mar 2026 - 9:29

score 110 · Answer 8 · 2026-03-25 11:06:39

110

Views

What is the reason for so much big prof of Cayley-Hamilton theorem in Linear Algebra?

Published on 25 Mar 2026 - 11:06

score 266 · Answer 9 · 2026-04-15 05:16:44

266

Views

Proof that characteristic polynomial of matrices in certain form is product of characteristic polynomials of sub-matrices

Published on 15 Apr 2026 - 5:16

score 207 · Answer 10 · 2026-03-25 09:24:30

207

Views

Non-Homogenous differential equation with complex roots and duality

Published on 25 Mar 2026 - 9:24

score 190 · Answer 11 · 2026-03-25 10:53:40

190

Views

Characteristic polynomial for the rank-$1$ perturbation

Published on 25 Mar 2026 - 10:53

score 71 · Answer 12 · 2026-03-25 09:28:52

71

Views

Why is there a reduction to REF to find the characteristic polynomial of a 4x4 matrix?

Published on 25 Mar 2026 - 9:28

score 52 · Answer 13 · 2026-03-25 10:53:38

52

Views

Matrix with characteristic equation equal to the rows of pascal triangle

Published on 25 Mar 2026 - 10:53

score 187 · Answer 14 · 2026-05-10 15:16:21

187

Views

Find the rational form of the given matrix

Published on 10 May 2026 - 15:16

score 40 · Answer 15 · 2026-03-25 11:06:39

40

Views

The form of the characteristic polynomial of matrices with eigenvalues 0 and 1

Published on 25 Mar 2026 - 11:06

List Question

Any smart approach to finding a matrix given the characteristic polynomial?

Find all $n$ for which there exist A, B, matrices of size n with real entries, such that $A^2B-BA^2=A$.

If $A^3+2A^2+2A+I_n=0_n$, then $\det(A)=-1$, where $A$ is a square matrix of odd size, with real entries

How to find the matrix of an endomorphism in a cyclic basis?

There is a polynomial $g(x)\in\mathbb{R}[x_1,..., x_n]$ such that $f(X) = g(a_0,..., a_{n−1})$ where $a_i$ is the coefficient of $λ^i$

Eigenvalues of a certain block matrix

Show that $p_\rho(λ) = p_{\rho_1}(λ)p_{\rho_2}(λ)$ where $p_\rho,p_{\rho_1},p_{\rho_2}$ are the characteristic polynomials.

What is the reason for so much big prof of Cayley-Hamilton theorem in Linear Algebra?

Proof that characteristic polynomial of matrices in certain form is product of characteristic polynomials of sub-matrices

Non-Homogenous differential equation with complex roots and duality

Characteristic polynomial for the rank-$1$ perturbation

Why is there a reduction to REF to find the characteristic polynomial of a 4x4 matrix?

Matrix with characteristic equation equal to the rows of pascal triangle

Find the rational form of the given matrix

The form of the characteristic polynomial of matrices with eigenvalues 0 and 1

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