List questions from matrix-analysis

Published on 11 Apr 2026 - 3:32

99

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How obtain the partial derivative of quadratic function $f(z)=\frac{1}{2} x^T(z)Q(z)x(z)$?

Published on 14 Apr 2026 - 13:12

302

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Intuition behind factorisation in Schur Complement Lemma proof

Published on 25 Mar 2026 - 12:52

176

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How do I prove that $\sum_{i,j=1}^na_{ij}b_{ij} \geq 0$ if $A=(a_{ij})$ and $B=(b_{ij})$ are both positive semidefinite $n \times n$ matrices?

Published on 25 Mar 2026 - 12:51

66

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

Published on 13 Apr 2026 - 6:14

52

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Let $Q,P$ be square row stochastic matrices with nonnegative real eigenvalues. Is $ || (2Q-I)(2P-I)||_\infty \leq 3 $?

Published on 15 Apr 2026 - 9:42

227

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Subgradient of function $f_p(\mathbf{A})$ that has as output the $p^{th}$ largest singular value

Published on 15 Apr 2026 - 7:45

58

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Dilation of a contraction in the connection with numerical range.

Published on 12 Apr 2026 - 14:04

434

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Ordering of positive semidefinite matrices

Published on 24 Apr 2026 - 9:34

41

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Perturbation of a matrix and eigen values

Published on 10 Apr 2026 - 7:23

81

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Approximation of selfadjoint matrix in $M_n(\mathbb{C})$

Published on 30 Apr 2026 - 23:12

628

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Show that if $g(x) = f(Ax + b)$, then $\delta g(x) = A^T \delta f(Ax + b)$

Published on 07 May 2026 - 14:30

59

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Inclusion of numerical range and translation and rotation invariance

Published on 13 Apr 2026 - 21:02

173

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Show that the smallest eigenvalue is strictly positive.

Published on 27 Mar 2026 - 21:23

337

Views

Two results of monotone operators of matrices

Published on 10 Dec 2019 - 19:55

List Question

Conjecture about $(0,1)$-matrices

How obtain the partial derivative of quadratic function $f(z)=\frac{1}{2} x^T(z)Q(z)x(z)$?

Intuition behind factorisation in Schur Complement Lemma proof

How do I prove that $\sum_{i,j=1}^na_{ij}b_{ij} \geq 0$ if $A=(a_{ij})$ and $B=(b_{ij})$ are both positive semidefinite $n \times n$ matrices?

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

Let $Q,P$ be square row stochastic matrices with nonnegative real eigenvalues. Is $ || (2Q-I)(2P-I)||_\infty \leq 3 $?

Subgradient of function $f_p(\mathbf{A})$ that has as output the $p^{th}$ largest singular value

Dilation of a contraction in the connection with numerical range.

Ordering of positive semidefinite matrices

Perturbation of a matrix and eigen values

Approximation of selfadjoint matrix in $M_n(\mathbb{C})$

Show that if $g(x) = f(Ax + b)$, then $\delta g(x) = A^T \delta f(Ax + b)$

Inclusion of numerical range and translation and rotation invariance

Show that the smallest eigenvalue is strictly positive.

Two results of monotone operators of matrices

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