List questions from positive-semidefinite

Published on 14 Jan 2020 - 22:22

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What assumption on $x$ is needed for $x x^\top$ to be positive definite?

Published on 23 Feb 2026 - 7:09

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Proving a symmetric Cauchy matrix is positive semidefinite

Published on 20 Mar 2026 - 4:33

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If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \leq A \leq B$, then det $A \leq$ det $B$.

Published on 20 Jan 2020 - 0:29

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If $0 \le A \le B$ then $\sqrt{A} \le \sqrt{B}$

Published on 21 Jan 2020 - 2:24

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Mean of (more than) two rank-1 positive semi-definite matrices

Published on 21 Jan 2020 - 8:01

80

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Why is $x^T(uu^T)x=(x^Tu)(u^Tx) = (\langle x, u \rangle)(\langle x, u \rangle)=((\langle x, u \rangle))^2 \geq 0$

Published on 26 Mar 2026 - 4:53

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What happened to the $2x_2^2-2x_1^2 part$?

Published on 23 Jan 2020 - 13:22

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Check 3x3 or above matrix is positive semidefinite

Published on 23 Jan 2020 - 20:51

165

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A quadratic inequality related to the $\log$ function

Published on 24 Jan 2020 - 5:02

46

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Is $L = \operatorname{diag}(R\mathbf{1})-R$ a PSD matrix?

Published on 24 Jan 2020 - 18:31

31

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Role of $f(\mathbf{x}_0)$ and $\nabla f(\mathbf{x}_0)^T (\mathbf{x} - \mathbf{x}_0)$ in quadratic approximation

Published on 24 Jan 2020 - 21:42

38

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Proof of, or constraints for, a matrix to be positive semidefinite

Published on 26 Jan 2020 - 12:09

68

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Intuition For Positive Semidefinite Metric Spaces

Published on 27 Jan 2020 - 5:59

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Convexity of $\{x\in \mathbb R^n,\;x^TAx\leq t\}$ for all $t$ implies that $A$ is p.s.d.

Published on 30 Jan 2020 - 18:12

List Question

Positive semi-definite matrix proof

What assumption on $x$ is needed for $x x^\top$ to be positive definite?

Proving a symmetric Cauchy matrix is positive semidefinite

If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \leq A \leq B$, then det $A \leq$ det $B$.

If $0 \le A \le B$ then $\sqrt{A} \le \sqrt{B}$

Mean of (more than) two rank-1 positive semi-definite matrices

Why is $x^T(uu^T)x=(x^Tu)(u^Tx) = (\langle x, u \rangle)(\langle x, u \rangle)=((\langle x, u \rangle))^2 \geq 0$

What happened to the $2x_2^2-2x_1^2 part$?

Check 3x3 or above matrix is positive semidefinite

A quadratic inequality related to the $\log$ function

Is $L = \operatorname{diag}(R\mathbf{1})-R$ a PSD matrix?

Role of $f(\mathbf{x}_0)$ and $\nabla f(\mathbf{x}_0)^T (\mathbf{x} - \mathbf{x}_0)$ in quadratic approximation

Proof of, or constraints for, a matrix to be positive semidefinite

Intuition For Positive Semidefinite Metric Spaces

Convexity of $\{x\in \mathbb R^n,\;x^TAx\leq t\}$ for all $t$ implies that $A$ is p.s.d.

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