Question

$\begin{bmatrix} A_{11} & A_{12}\\ A^* _{12} &A_{22} \end{bmatrix} $ is positive semidefinite, then $N(A^* _{11}) \subset N(A^* _{12})$

score 41 · Answer 1 · 2022-11-11 13:54:43

$\begin{bmatrix} A_{11} & A_{12}\\ A^* _{12} &A_{22} \end{bmatrix} $ is positive semidefinite, then $N(A^* _{11}) \subset N(A^* _{12})$

score 90 · Answer 2 · 2026-03-25 23:09:03

90

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score 50 · Answer 5 · 2022-11-29 20:18:49

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score 113 · Answer 6 · 2026-03-27 16:26:18

113

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List Question

$\begin{bmatrix} A_{11} & A_{12}\\ A^* _{12} &A_{22} \end{bmatrix} $ is positive semidefinite, then $N(A^* _{11}) \subset N(A^* _{12})$

Jacobian of Proximal Operator is Positive Semidefinite

Inverse of sum of matrices has lower norm than the inverse of summand(s)

Replacing $I$ with S.P.D. $B$ in ridge regression, is the norm still bounded by OLS?

Let $ A \in \mathbb R^{n \times n} $ be a positive semidefinite matrix, and let $x, y \in \mathbb R^n $. If $\langle x, y \rangle \geq 0 $ then ...

Do Positive Eigenvalues (or Spectrum) of an Operator on Hilbert Space Imply Positivity

numerical radius

Proof or confutation that a matrix is positive semidefinite

Decomposition of hermitian matrix as difference of positive semidefinite matrices

Prove that $A^{-1} - X(X'AX)^{-1}X'$ is positive semidefinite

Checking the positive semi-definiteness of the square of a matrix

Positive definiteness of graph Laplacian

Proof that a matrix consisting of minima is positive-semidefinite

the uniqueness of the decomposition of a rank 1 PSD matrix into the product to two vectors

How can a scaling factor determine positive semi-definiteness?

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