List questions from determinant

Published on 25 Mar 2026 - 4:44

94

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Trace of $3 \times 3$ matrix A and the polynomial $p(z)=det(z\cdot I_{3} - A)$.

Published on 09 Nov 2018 - 1:02

136

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Linearly dependent rows and adjoint

Published on 09 Nov 2018 - 5:54

182

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Determinant of a random symmetric matrix

Published on 25 Mar 2026 - 11:10

398

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Matrix determinant effect

Published on 09 Nov 2018 - 17:51

283

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Is there a non-constructive proof that the determinant exists?

Published on 09 Nov 2018 - 20:34

127

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Trace inequality for a symmetric matrix

Published on 26 Mar 2026 - 13:50

80

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Calculating the Wronskian of five functions by hand

Published on 09 Nov 2018 - 23:14

129

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Property of determinant with Leibniz formula

Published on 10 Nov 2018 - 16:08

715

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Requirement that determinant be zero for characteristic polynomial

Published on 11 Nov 2018 - 4:59

152

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Show that $\det\left[\begin{smallmatrix}1&\cos a&\cos b\\ \cos a&1&\cos(a+b) \\ \cos b&\cos(a+b)&1 \end{smallmatrix}\right]=0$

Published on 12 Nov 2018 - 7:17

23

Views

For a positive semi-definite $d\times d$ matrix $A$, $ (\text{det}(AS))^{\frac{1}{d}}\leq\frac{1}{d}\text{Tr}(AS) $ for every $S\in\text{SPD}_{d}$.

Published on 25 Mar 2026 - 16:08

197

Views

$f(X^1,...,X^n)=\det[X^1...X^n]$ is differentiable

Published on 13 Nov 2018 - 10:26

78

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Proving that $det(A) \ne 0$ with $A$ satisfying following conditions.

Published on 14 Nov 2018 - 4:43

964

Views

Solving Vandermonde equation system

Published on 14 Nov 2018 - 15:16

List Question

Lagrange identity for determinants

Trace of $3 \times 3$ matrix A and the polynomial $p(z)=det(z\cdot I_{3} - A)$.

Linearly dependent rows and adjoint

Determinant of a random symmetric matrix

Matrix determinant effect

Is there a non-constructive proof that the determinant exists?

Trace inequality for a symmetric matrix

Calculating the Wronskian of five functions by hand

Property of determinant with Leibniz formula

Requirement that determinant be zero for characteristic polynomial

Show that $\det\left[\begin{smallmatrix}1&\cos a&\cos b\\ \cos a&1&\cos(a+b) \\ \cos b&\cos(a+b)&1 \end{smallmatrix}\right]=0$

For a positive semi-definite $d\times d$ matrix $A$, $ (\text{det}(AS))^{\frac{1}{d}}\leq\frac{1}{d}\text{Tr}(AS) $ for every $S\in\text{SPD}_{d}$.

$f(X^1,...,X^n)=\det[X^1...X^n]$ is differentiable

Proving that $det(A) \ne 0$ with $A$ satisfying following conditions.

Solving Vandermonde equation system

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