Question

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

score 183 · Answer 1 · 2020-01-27 16:17:40

183

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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 27 Jan 2020 - 16:17

score 79 · Answer 2 · 2020-01-29 18:42:42

79

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Diagonalizability of a matrix

Published on 29 Jan 2020 - 18:42

score 64 · Answer 3 · 2020-01-31 21:06:56

64

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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 31 Jan 2020 - 21:06

score 34 · Answer 4 · 2020-02-02 12:25:55

34

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

Published on 02 Feb 2020 - 12:25

score 109 · Answer 5 · 2020-02-07 14:19:34

109

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

Published on 07 Feb 2020 - 14:19

score 117 · Answer 6 · 2020-02-08 10:43:55

117

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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 08 Feb 2020 - 10:43

score 127 · Answer 7 · 2026-03-22 07:36:59

127

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

Published on 22 Mar 2026 - 7:36

score 1k · Answer 8 · 2020-02-14 01:52:40

1k

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

Published on 14 Feb 2020 - 1:52

score 385 · Answer 9 · 2020-02-20 18:46:41

385

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

Published on 20 Feb 2020 - 18:46

score 656 · Answer 10 · 2020-02-21 02:29:47

656

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Proving characteristic polynomial and invertibility

Published on 21 Feb 2020 - 2:29

score 396 · Answer 11 · 2020-02-21 21:07:08

396

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

Published on 21 Feb 2020 - 21:07

score 766 · Answer 12 · 2020-02-22 06:31:24

766

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

Published on 22 Feb 2020 - 6:31

score 79 · Answer 13 · 2020-02-27 11:31:19

79

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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 27 Feb 2020 - 11:31

score 52 · Answer 14 · 2020-02-27 20:40:13

52

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Question of defining characteristic polynomials differently

Published on 27 Feb 2020 - 20:40

score 136 · Answer 15 · 2020-02-27 23:06:01

136

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

Published on 27 Feb 2020 - 23:06

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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