Question

The characteristic polynomial of an ODE is equal to the characteristic polynomial of the companion matrix

score 155 · Answer 1 · 2020-11-09 10:24:50

155

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The characteristic polynomial of an ODE is equal to the characteristic polynomial of the companion matrix

Published on 09 Nov 2020 - 10:24

score 134 · Answer 2 · 2020-11-09 21:04:49

134

Views

How to prove that all the roots $x_0$ of $p_n(x) = \frac{x}{f(n)} \sum\limits_{k=1}^n a_k p_{n-k}(x)$ satisfy $- \frac{4d}{a_1^2} f(n) < x_0 \leq 0$?

Published on 09 Nov 2020 - 21:04

score 22 · Answer 3 · 2020-11-12 10:57:24

22

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Finding the power of a complex valued matrix with only the characteristic polynomial

Published on 12 Nov 2020 - 10:57

score 720 · Answer 4 · 2020-11-18 22:15:14

720

Views

How to find the eigenvalues of $x x^T - y y^T$?

Published on 18 Nov 2020 - 22:15

score 169 · Answer 5 · 2020-11-20 02:20:35

169

Views

Greatest common divisor of Characteristic Polynomials

Published on 20 Nov 2020 - 2:20

score 115 · Answer 6 · 2020-11-20 03:37:11

115

Views

Determinants and Characteristic Polynomial of Matrices

Published on 20 Nov 2020 - 3:37

score 225 · Answer 7 · 2020-11-20 09:48:22

225

Views

Given the characteristic (and minimal) polynomial of $T:V\to V$, how many distinct Jordan forms are possible?

Published on 20 Nov 2020 - 9:48

score 56 · Answer 8 · 2020-11-21 04:14:57

56

Views

Relation between characteristic polynomials of $A$ and the linear map $\mathscr{L}(X)=AX$

Published on 21 Nov 2020 - 4:14

score 454 · Answer 9 · 2020-11-24 12:28:44

454

Views

A $4 \times 4$ matrix over $\mathbb{C}$ such that rank$(A)=2$ and $A^3 =A^2 \neq 0$ and $A$ is not diagonalizable

Published on 24 Nov 2020 - 12:28

score 105 · Answer 10 · 2020-12-04 16:03:43

105

Views

Series of characteristic polynomials

Published on 04 Dec 2020 - 16:03

score 318 · Answer 11 · 2020-12-05 06:01:12

318

Views

Show that no non-trivial $T$ -invariant subspace has a complementary $T$ -invariant subspace

Published on 05 Dec 2020 - 6:01

score 184 · Answer 12 · 2026-03-25 19:03:23

184

Views

Show that two matrices are similar when they have the same characteristic polynomial and a cyclic vector

Published on 25 Mar 2026 - 19:03

score 867 · Answer 13 · 2020-12-14 01:20:28

867

Views

$A$ is diagonalizable if the minimal and characteristic polynomial of $A$ are equal.

Published on 14 Dec 2020 - 1:20

score 142 · Answer 14 · 2020-12-15 05:36:59

142

Views

Computing the characteristic polynomial of a linear transformation

Published on 15 Dec 2020 - 5:36

score 930 · Answer 15 · 2020-12-15 11:21:16

930

Views

Finding matrices for which $x^2+1$ is the minimal polynomial

Published on 15 Dec 2020 - 11:21

List Question

The characteristic polynomial of an ODE is equal to the characteristic polynomial of the companion matrix

How to prove that all the roots $x_0$ of $p_n(x) = \frac{x}{f(n)} \sum\limits_{k=1}^n a_k p_{n-k}(x)$ satisfy $- \frac{4d}{a_1^2} f(n) < x_0 \leq 0$?

Finding the power of a complex valued matrix with only the characteristic polynomial

How to find the eigenvalues of $x x^T - y y^T$?

Greatest common divisor of Characteristic Polynomials

Determinants and Characteristic Polynomial of Matrices

Given the characteristic (and minimal) polynomial of $T:V\to V$, how many distinct Jordan forms are possible?

Relation between characteristic polynomials of $A$ and the linear map $\mathscr{L}(X)=AX$

A $4 \times 4$ matrix over $\mathbb{C}$ such that rank$(A)=2$ and $A^3 =A^2 \neq 0$ and $A$ is not diagonalizable

Series of characteristic polynomials

Show that no non-trivial $T$ -invariant subspace has a complementary $T$ -invariant subspace

Show that two matrices are similar when they have the same characteristic polynomial and a cyclic vector

$A$ is diagonalizable if the minimal and characteristic polynomial of $A$ are equal.

Computing the characteristic polynomial of a linear transformation

Finding matrices for which $x^2+1$ is the minimal polynomial

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