Question

Does $A\geq (\mathrm{tr}(A^{-1}))^{-1}I$ hold for symmetric positive-definite matrix $A$?

score 53 · Answer 1 · 2026-03-26 17:13:18

53

Views

Does $A\geq (\mathrm{tr}(A^{-1}))^{-1}I$ hold for symmetric positive-definite matrix $A$?

Published on 26 Mar 2026 - 17:13

score 73 · Answer 2 · 2026-03-26 19:00:45

73

Views

On $Z (X) = \text{trace}((X^TA_1X)^{-1}X^TA_2X)$

Published on 26 Mar 2026 - 19:00

score 35 · Answer 3 · 2026-03-26 09:18:06

35

Views

Let $V = \{ A \in M_{2}(\mathbb{R}) \colon tr(A) = 0\}$. If $f \in V^{\circ}$ then prove that $f(I) = 0 \Rightarrow f = 0.$

Published on 26 Mar 2026 - 9:18

score 1.7k · Answer 4 · 2026-03-25 18:55:40

1.7k

Views

Trace of a square root of two matrices

Published on 25 Mar 2026 - 18:55

score 213 · Answer 5 · 2026-03-25 17:39:41

213

Views

Product of a nilpotent matrix and a diagonal PD matrix

Published on 25 Mar 2026 - 17:39

score 104 · Answer 6 · 2026-03-25 16:03:45

104

Views

$\operatorname{Tr}\det H$ of a $2\times 2$ block matrix $H$

Published on 25 Mar 2026 - 16:03

score 78 · Answer 7 · 2026-03-25 18:57:45

78

Views

Positivity of trace of some product of matrices

Published on 25 Mar 2026 - 18:57

score 143 · Answer 8 · 2019-09-03 17:07:57

143

Views

Prove that $A^5 \neq I$

Published on 03 Sep 2019 - 17:07

score 64 · Answer 9 · 2026-03-25 12:49:48

64

Views

The relation between the trace of a positive definite matrix and the trace of the inverse of this matrix

Published on 25 Mar 2026 - 12:49

score 475 · Answer 10 · 2019-09-11 03:55:20

475

Views

For $A \in \mathcal{M}_3(\mathbb{C})$, does $\mathrm{tr}(A^2) = \mathrm{tr}(A^3) \in \mathbb{Q}$ imply $\mathrm{tr}(A^4) \in \mathbb{Q}$?

Published on 11 Sep 2019 - 3:55

score 117 · Answer 11 · 2019-09-14 08:12:24

117

Views

Semisimplicity of $\mathfrak{sp}(2n)$ via non-degeneracy of the Killing Form.

Published on 14 Sep 2019 - 8:12

score 369 · Answer 12 · 2026-02-23 06:04:04

369

Views

When is the trace of an integral element of an algebra integral?

Published on 23 Feb 2026 - 6:04

score 408 · Answer 13 · 2019-09-16 10:56:35

408

Views

trace on direct sum

Published on 16 Sep 2019 - 10:56

score 230 · Answer 14 · 2019-09-16 15:23:50

230

Views

Differentiation of Scalar with respect to Vector, Second Order, involving Hadamard Products

Published on 16 Sep 2019 - 15:23

score 81 · Answer 15 · 2019-09-17 04:00:03

81

Views

Some relations between multi-trace combinations

Published on 17 Sep 2019 - 4:00

List Question

Does $A\geq (\mathrm{tr}(A^{-1}))^{-1}I$ hold for symmetric positive-definite matrix $A$?

On $Z (X) = \text{trace}((X^TA_1X)^{-1}X^TA_2X)$

Let $V = \{ A \in M_{2}(\mathbb{R}) \colon tr(A) = 0\}$. If $f \in V^{\circ}$ then prove that $f(I) = 0 \Rightarrow f = 0.$

Trace of a square root of two matrices

Product of a nilpotent matrix and a diagonal PD matrix

$\operatorname{Tr}\det H$ of a $2\times 2$ block matrix $H$

Positivity of trace of some product of matrices

Prove that $A^5 \neq I$

The relation between the trace of a positive definite matrix and the trace of the inverse of this matrix

For $A \in \mathcal{M}_3(\mathbb{C})$, does $\mathrm{tr}(A^2) = \mathrm{tr}(A^3) \in \mathbb{Q}$ imply $\mathrm{tr}(A^4) \in \mathbb{Q}$?

Semisimplicity of $\mathfrak{sp}(2n)$ via non-degeneracy of the Killing Form.

When is the trace of an integral element of an algebra integral?

trace on direct sum

Differentiation of Scalar with respect to Vector, Second Order, involving Hadamard Products

Some relations between multi-trace combinations

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