List questions from trace

Published on 05 Jan 2016 - 17:58

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Rank = trace for idempotent nonsymmetric matrices

Published on 05 Jan 2016 - 20:25

650

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Show that $rank(A) \ngeq \frac{[tr(A)]^2 }{tr(A^2)}$

Published on 07 Jan 2016 - 22:34

792

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Find the inverse and determinant of A=(aI +T),

Published on 08 Jan 2016 - 1:04

298

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Trace inequality on positive matrices

Published on 11 Jan 2016 - 12:16

361

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Trace inequality $tr(|XY|) \leq \|X\| tr(|Y|) $

Published on 14 Jan 2016 - 23:00

16.3k

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Trace and the coefficients of the characteristic polynomial of a matrix

Published on 18 Jan 2016 - 15:00

894

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Cayley-Hamilton Theorem - Trace of Exterior Power Form

Published on 28 Mar 2026 - 15:25

1.3k

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Dimension of trace-subspace

Published on 29 Jan 2016 - 10:23

2.6k

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Trace of the $k$-th Exterior Power of a Linear Operator

Published on 28 Mar 2026 - 15:20

793

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Can we say that $\det(A+B) = \det(A) + \det(B) +\operatorname{tr}(A) \operatorname{tr}(B) - \operatorname{tr}(AB)$?

Published on 05 Feb 2016 - 16:47

23

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the numbers Tr$(X^n)$ determine the conjugacy class of semisimple $X \in GL_n(\mathbb{C})$.

Published on 08 Feb 2016 - 11:09

59

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Trace of an algebraic number

Published on 11 Feb 2016 - 4:42

75

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Find $\lim_a \frac{Tr^n \left( ({\bf x}-a\cdot{\bf y}) \cdot ({\bf x}-a \cdot{\bf y})^T \right)-Tr^n \left( {\bf x} \cdot {\bf x}^T \right)}{a}$

Published on 11 Feb 2016 - 23:23

147

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Is it true that for all matrices $A$ and all traceless matrices $T$, there exists a traceless matrix $T'$ such that $AT = T'A$?

Published on 12 Feb 2016 - 17:19

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How to Trace a Real-Life Flower Using Polar Equations?

Rank = trace for idempotent nonsymmetric matrices

Show that $rank(A) \ngeq \frac{[tr(A)]^2 }{tr(A^2)}$

Find the inverse and determinant of A=(aI +T),

Trace inequality on positive matrices

Trace inequality $tr(|XY|) \leq \|X\| tr(|Y|) $

Trace and the coefficients of the characteristic polynomial of a matrix

Cayley-Hamilton Theorem - Trace of Exterior Power Form

Dimension of trace-subspace

Trace of the $k$-th Exterior Power of a Linear Operator

Can we say that $\det(A+B) = \det(A) + \det(B) +\operatorname{tr}(A) \operatorname{tr}(B) - \operatorname{tr}(AB)$?

the numbers Tr$(X^n)$ determine the conjugacy class of semisimple $X \in GL_n(\mathbb{C})$.

Trace of an algebraic number

Find $\lim_a \frac{Tr^n \left( ({\bf x}-a\cdot{\bf y}) \cdot ({\bf x}-a \cdot{\bf y})^T \right)-Tr^n \left( {\bf x} \cdot {\bf x}^T \right)}{a}$

Is it true that for all matrices $A$ and all traceless matrices $T$, there exists a traceless matrix $T'$ such that $AT = T'A$?

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