List questions from schur-complement | MathQa

Is the ellipsoid $x'Qx < \alpha$ equivalent to $\alpha Q^{-1} - x x' \succ 0$?

Published on 12 Jan 2025 - 19:23

Relationship between rank and positive semidefiniteness

Published on 05 Jan 2025 - 18:48

Formulating a convex optimization problem as semidefinite program

Published on 12 Jan 2025 - 9:15

Does a certain matrix inequality imply that a matrix is negative definite?

Published on 12 Jan 2025 - 9:26

If a matrix has eigenvalues with non-zero real parts, can the eigenvalues of its Schur complement be arbitrarily close to zero?

Published on 12 Jan 2025 - 9:26

How to compute the determinant of this block matrix?

Published on 12 Jan 2025 - 9:26

How to prove that the Schur complement of symmetric, positive-definite matrix is positive-definite?

Published on 12 Jan 2025 - 9:26

$C= A\oplus B$. Then prove that $C$ is diagonalisable if and only if both $ A$ and $B$ are diagonalisable.

Published on 12 Jan 2025 - 9:26

Positive semidefiniteness of block matrix when diagonal blocks are not invertible

Published on 12 Jan 2025 - 9:26

Eigenvalues of the Schur complement

Published on 12 Jan 2025 - 9:26