List questions from positive-definite

Published on 02 Jul 2020 - 12:42

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On positive definite matrices and eigenvalues

Published on 04 Jul 2020 - 18:12

619

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What is the image of $x^{\rm T}Qx\le 1$ under a linear map $x \mapsto Cx$?

Published on 26 Mar 2026 - 21:10

714

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Choosing a regularization parameter to ensure positive definite-ness.

Published on 25 Mar 2026 - 16:45

5k

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invertible matrices are positive definite?

Published on 07 Jul 2020 - 23:01

683

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Prove that a positive operator is invertible

Published on 27 Mar 2026 - 16:12

236

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Bounds on entries of matrix inverse

Published on 26 Mar 2026 - 6:07

94

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If $A \leq B$ for a positive-definite operator $A$ in finite dimensions, then $B^{-1} \leq A^{-1}$

Published on 25 Mar 2026 - 20:36

1.4k

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Inverse of sum of inverses of matrices

Published on 15 Jul 2020 - 10:08

268

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Property of symmetric positive definite related to diagonal entries and gaussian elimination

Published on 26 Mar 2026 - 9:26

80

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Is $AA^\ast \preceq B^\ast B$ implies $\bar{\sigma}(A)\le \underline{\sigma}(B)$

Published on 16 Jul 2020 - 15:59

74

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For which values the matrix $ B = \Big(\begin{matrix} A & -A\\ -A & \alpha A \end{matrix}\Big)$ results positive definite (strict)?

Published on 25 Mar 2026 - 8:09

98

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Given $A,B$ symmetric positive definite matrices, is $B^{-1}A$ always symmetric positive definite?

Published on 21 Jul 2020 - 5:01

221

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Find the smallest eigenvalue of $G=[ \exp(-(x_i-x_j )^2]_{i,j}$ for ${\bf x}=[x_1,\dots,x_n]$

Published on 22 Jul 2020 - 18:52

176

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Orthogonal projections of real positive definite matrices and their determinants

Published on 23 Jul 2020 - 11:07

List Question

Positive definite matrices?

On positive definite matrices and eigenvalues

What is the image of $x^{\rm T}Qx\le 1$ under a linear map $x \mapsto Cx$?

Choosing a regularization parameter to ensure positive definite-ness.

invertible matrices are positive definite?

Prove that a positive operator is invertible

Bounds on entries of matrix inverse

If $A \leq B$ for a positive-definite operator $A$ in finite dimensions, then $B^{-1} \leq A^{-1}$

Inverse of sum of inverses of matrices

Property of symmetric positive definite related to diagonal entries and gaussian elimination

Is $AA^\ast \preceq B^\ast B$ implies $\bar{\sigma}(A)\le \underline{\sigma}(B)$

For which values the matrix $ B = \Big(\begin{matrix} A & -A\\ -A & \alpha A \end{matrix}\Big)$ results positive definite (strict)?

Given $A,B$ symmetric positive definite matrices, is $B^{-1}A$ always symmetric positive definite?

Find the smallest eigenvalue of $G=[ \exp(-(x_i-x_j )^2]_{i,j}$ for ${\bf x}=[x_1,\dots,x_n]$

Orthogonal projections of real positive definite matrices and their determinants

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