Question

Prove the alternating property of the function $\det$.

score 179 · Answer 1 · 2023-06-19 04:33:56

179

Views

Prove the alternating property of the function $\det$.

Published on 19 Jun 2023 - 4:33

score 93 · Answer 2 · 2026-04-09 19:47:29

93

Views

How to understand the dual of determinants

Published on 09 Apr 2026 - 19:47

score 117 · Answer 3 · 2026-04-08 09:39:11

117

Views

If $n\times n$ matrix $A$ satisfies $A^2+2A-3E=O$, show that $A$ is invertible.

Published on 08 Apr 2026 - 9:39

score 283 · Answer 4 · 2026-03-27 17:40:27

283

Views

Why cross product gives area of parallelogram formed by two vectors

Published on 27 Mar 2026 - 17:40

score 75 · Answer 5 · 2023-06-21 16:20:40

75

Views

1 row matrix determinant

Published on 21 Jun 2023 - 16:20

score 30 · Answer 6 · 2023-06-22 08:11:00

30

Views

Prove that $\det(VH'BH+I_n)=\det(BHVH'+I_p)$

Published on 22 Jun 2023 - 8:11

score 43 · Answer 7 · 2026-03-25 14:46:54

43

Views

Prime numbers as zeros of polynomials from the determinant of the form $P(x,N)=|\log(x) \gcd (n,k)-\phi (n)\log(\gcd (n,k))|$

Published on 25 Mar 2026 - 14:46

score 2.7k · Answer 8 · 2026-03-26 02:58:20

2.7k

Views

If two matrices have the same characteristic polynomial then do they have the same determinant?

Published on 26 Mar 2026 - 2:58

score 69 · Answer 9 · 2023-06-25 20:52:01

69

Views

If matrix $A,B$ have null determinant, then there exists a matrix $X$ such that $AX = XB = 0$

Published on 25 Jun 2023 - 20:52

score 99 · Answer 10 · 2023-06-25 21:49:46

99

Views

Show that last term of the characteristic polynomial of $A$ is $(-1)^n \det A$, and that the term of degree $(n-1)$ is $Tr (A)$.

Published on 25 Jun 2023 - 21:49

score 135 · Answer 11 · 2026-03-26 04:36:22

135

Views

Prove or disprove $\det(6(A^3 + B^3 + C^3)+(A+B+C)^3) \ge 5^2\det(A^2 + B^2 + C^2)\cdot\det(A + B+ C)$

Published on 26 Mar 2026 - 4:36

score 139 · Answer 12 · 2026-04-11 15:30:05

139

Views

Relationship between determinant and trace of a matrix

Published on 11 Apr 2026 - 15:30

score 36 · Answer 13 · 2026-04-10 23:52:28

36

Views

How to prove that determinant of a linear map measures the change of volume and orientation of any measurable set.

Published on 10 Apr 2026 - 23:52

score 80 · Answer 14 · 2026-03-26 19:01:47

80

Views

My calulations show that for all $n\times m$ matrices $A, B$, it is $det(A^tB)=0$. Where is the mistake?

Published on 26 Mar 2026 - 19:01

score 28 · Answer 15 · 2023-07-04 10:09:16

Let $A,B\in M_{2\times2}\left(\mathbb{F}\right)$ such that $\det A\neq0$ and $\det B=2$. Calculate $\det\left(5AB^{3}A^{-1}B^{-1}\right)$.

List Question

Prove the alternating property of the function $\det$.

How to understand the dual of determinants

If $n\times n$ matrix $A$ satisfies $A^2+2A-3E=O$, show that $A$ is invertible.

Why cross product gives area of parallelogram formed by two vectors

1 row matrix determinant

Prove that $\det(VH'BH+I_n)=\det(BHVH'+I_p)$

Prime numbers as zeros of polynomials from the determinant of the form $P(x,N)=|\log(x) \gcd (n,k)-\phi (n)\log(\gcd (n,k))|$

If two matrices have the same characteristic polynomial then do they have the same determinant?

If matrix $A,B$ have null determinant, then there exists a matrix $X$ such that $AX = XB = 0$

Show that last term of the characteristic polynomial of $A$ is $(-1)^n \det A$, and that the term of degree $(n-1)$ is $Tr (A)$.

Prove or disprove $\det(6(A^3 + B^3 + C^3)+(A+B+C)^3) \ge 5^2\det(A^2 + B^2 + C^2)\cdot\det(A + B+ C)$

Relationship between determinant and trace of a matrix

How to prove that determinant of a linear map measures the change of volume and orientation of any measurable set.

My calulations show that for all $n\times m$ matrices $A, B$, it is $det(A^tB)=0$. Where is the mistake?

Let $A,B\in M_{2\times2}\left(\mathbb{F}\right)$ such that $\det A\neq0$ and $\det B=2$. Calculate $\det\left(5AB^{3}A^{-1}B^{-1}\right)$.

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