Question

$ A^2 - B^2 = I_{2n+1} \implies det(AB-BA)=0 $ where A,B are complex matrices of odd size

score 184 · Answer 1 · 2026-03-25 06:05:37

184

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$ A^2 - B^2 = I_{2n+1} \implies det(AB-BA)=0 $ where A,B are complex matrices of odd size

Published on 25 Mar 2026 - 6:05

score 82 · Answer 2 · 2026-04-10 17:19:10

82

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Diagonalizability of a matrix

Published on 10 Apr 2026 - 17:19

score 65 · Answer 3 · 2026-03-25 06:06:52

65

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diagonalize the following n×n matrix. I am wondering if my solution for the characteristic polynomial is valid or if there is a better way to do it.

Published on 25 Mar 2026 - 6:06

score 35 · Answer 4 · 2026-03-25 07:47:31

35

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Characteristic polynomial in $\mathbb{C}^2$

Published on 25 Mar 2026 - 7:47

score 110 · Answer 5 · 2026-03-25 06:06:18

110

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Matrix representation and characterstic polynomial of linear transformation from the 0 vector space to a finitely-dimensional space

Published on 25 Mar 2026 - 6:06

score 118 · Answer 6 · 2026-03-25 07:46:25

118

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$ A^3 + B^2 = I_n $ and $A^5=A^2$, then $\det(A^2 + B^2 + I_n) \geq 0 $ and $\operatorname{rank}(I_n + AB^2) = \mathrm{rank}(I_n - AB^2) $

Published on 25 Mar 2026 - 7:46

score 129 · Answer 7 · 2026-04-06 00:47:18

129

Views

About the characteristic equation of a square matrix (Cayley-Hamilton theorem)

Published on 06 Apr 2026 - 0:47

score 1k · Answer 8 · 2026-03-25 06:06:33

1k

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Fibonacci closed form via vector space of infinite sequences of real numbers and geometric sequences

Published on 25 Mar 2026 - 6:06

score 386 · Answer 9 · 2026-03-25 06:04:22

386

Views

Question about the proving that Characteristic Polynomial Independent From the Choice of Basis

Published on 25 Mar 2026 - 6:04

score 657 · Answer 10 · 2026-03-25 07:34:31

657

Views

Proving characteristic polynomial and invertibility

Published on 25 Mar 2026 - 7:34

score 398 · Answer 11 · 2026-03-25 09:27:34

398

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If $A,B$ are diagonalisable, does $AB$ diagonalisable imply $BA$ diagonalisable?

Published on 25 Mar 2026 - 9:27

score 767 · Answer 12 · 2026-03-25 12:53:39

767

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Eigenvalues of $5 \times 5$ matrix with real entries from given condition

Published on 25 Mar 2026 - 12:53

score 80 · Answer 13 · 2026-03-25 07:45:43

80

Views

Why is $a_n(x) \neq 0$ for $a_n(x) = c_1 x a_{n-1}(x) + c_2 x a_{n-2}(x)$ if the discriminant of the characteristic polynomial $\Delta_{\lambda} > 0$?

Published on 25 Mar 2026 - 7:45

score 53 · Answer 14 · 2026-03-25 06:00:26

53

Views

Question of defining characteristic polynomials differently

Published on 25 Mar 2026 - 6:00

score 137 · Answer 15 · 2026-03-25 07:43:12

137

Views

Using characteristic polynomial for getting an asymptotic information to a recurrence relation with non-constant coefficient

Published on 25 Mar 2026 - 7:43

List Question

$ A^2 - B^2 = I_{2n+1} \implies det(AB-BA)=0 $ where A,B are complex matrices of odd size

Diagonalizability of a matrix

diagonalize the following n×n matrix. I am wondering if my solution for the characteristic polynomial is valid or if there is a better way to do it.

Characteristic polynomial in $\mathbb{C}^2$

Matrix representation and characterstic polynomial of linear transformation from the 0 vector space to a finitely-dimensional space

$ A^3 + B^2 = I_n $ and $A^5=A^2$, then $\det(A^2 + B^2 + I_n) \geq 0 $ and $\operatorname{rank}(I_n + AB^2) = \mathrm{rank}(I_n - AB^2) $

About the characteristic equation of a square matrix (Cayley-Hamilton theorem)

Fibonacci closed form via vector space of infinite sequences of real numbers and geometric sequences

Question about the proving that Characteristic Polynomial Independent From the Choice of Basis

Proving characteristic polynomial and invertibility

If $A,B$ are diagonalisable, does $AB$ diagonalisable imply $BA$ diagonalisable?

Eigenvalues of $5 \times 5$ matrix with real entries from given condition

Why is $a_n(x) \neq 0$ for $a_n(x) = c_1 x a_{n-1}(x) + c_2 x a_{n-2}(x)$ if the discriminant of the characteristic polynomial $\Delta_{\lambda} > 0$?

Question of defining characteristic polynomials differently

Using characteristic polynomial for getting an asymptotic information to a recurrence relation with non-constant coefficient

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