Question

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

score 256 · Answer 1 · 2020-02-29 07:56:21

256

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

Published on 29 Feb 2020 - 7:56

score 122 · Answer 2 · 2020-03-06 11:59:18

122

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 06 Mar 2020 - 11:59

score 87 · Answer 3 · 2020-03-13 12:15:37

87

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 13 Mar 2020 - 12:15

score 83 · Answer 4 · 2020-03-20 02:37:07

83

Views

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

Published on 20 Mar 2020 - 2:37

score 174 · Answer 5 · 2020-03-20 21:53:38

174

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 20 Mar 2020 - 21:53

score 83 · Answer 6 · 2020-03-23 00:45:27

83

Views

Eigenvalues of a certain block matrix

Published on 23 Mar 2020 - 0:45

score 30 · Answer 7 · 2020-03-24 23:53:56

30

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 24 Mar 2020 - 23:53

score 109 · Answer 8 · 2020-03-25 05:12:40

109

Views

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

Published on 25 Mar 2020 - 5:12

score 263 · Answer 9 · 2020-03-26 00:05:45

263

Views

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

Published on 26 Mar 2020 - 0:05

score 206 · Answer 10 · 2020-04-02 10:12:01

206

Views

Non-Homogenous differential equation with complex roots and duality

Published on 02 Apr 2020 - 10:12

score 189 · Answer 11 · 2020-04-04 13:27:50

189

Views

Characteristic polynomial for the rank-$1$ perturbation

Published on 04 Apr 2020 - 13:27

score 70 · Answer 12 · 2020-04-06 03:12:41

70

Views

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

Published on 06 Apr 2020 - 3:12

score 51 · Answer 13 · 2020-04-06 04:19:50

51

Views

Matrix with characteristic equation equal to the rows of pascal triangle

Published on 06 Apr 2020 - 4:19

score 184 · Answer 14 · 2020-04-07 12:18:10

184

Views

Find the rational form of the given matrix

Published on 07 Apr 2020 - 12:18

score 39 · Answer 15 · 2020-04-07 20:27:48

39

Views

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

Published on 07 Apr 2020 - 20:27

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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