Question

Positivity of a matrix built on Pascal's triangle

score 142 · Answer 1 · 2026-03-25 06:50:39

142

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Positivity of a matrix built on Pascal's triangle

Published on 25 Mar 2026 - 6:50

score 144 · Answer 2 · 2026-03-27 13:47:24

144

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An interesting property of positive definite and essentially non-negative matrix

Published on 27 Mar 2026 - 13:47

score 82 · Answer 3 · 2023-02-27 03:39:50

82

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If $A=B+C$, $A,B,C$ are semipositive definite matrices, prove that $\text{im}A=\text{im}B+\text{im}C$

Published on 27 Feb 2023 - 3:39

score 280 · Answer 4 · 2026-03-25 19:11:59

280

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Can we show the block matrix of the inverse of $A$ is greater than the inverse of the block matrix of $A$?

Published on 25 Mar 2026 - 19:11

score 94 · Answer 5 · 2023-03-04 14:11:26

94

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Is the symmetric matrix $vv^{T} - hI$ is strictly negative definite for all small enough $h>0$? Is $\det(vv^{T} - hI)<0$ for small positive $h?$

Published on 04 Mar 2023 - 14:11

score 56 · Answer 6 · 2026-03-25 06:48:09

56

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When is the inverse of a sparse SPD matrix also sparse?

Published on 25 Mar 2026 - 6:48

score 101 · Answer 7 · 2023-03-09 01:20:05

101

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If X is a symmetric diagonal dominant PD matrix, C and K are diagonal positive matrices. Can I find some bounds on C, K to make K(CX +I) PD?

Published on 09 Mar 2023 - 1:20

score 44 · Answer 8 · 2026-03-27 13:48:17

44

Views

Suppose A is a nonsymmetric PD matrix. K is a diagonal matrix, with all entries nonnegative, Can I find a bound of K such that $A^TA+KA+AK$ is PD?

Published on 27 Mar 2026 - 13:48

score 215 · Answer 9 · 2026-03-26 17:29:52

215

Views

Solving a quadratic program with simple linear constraints

Published on 26 Mar 2026 - 17:29

score 44 · Answer 10 · 2026-03-26 02:55:07

44

Views

Are these conditions sufficient to guarantee positive definiteness?

Published on 26 Mar 2026 - 2:55

score 18 · Answer 11 · 2023-03-14 22:20:44

18

Views

minima function is positive defined

Published on 14 Mar 2023 - 22:20

score 76 · Answer 12 · 2023-03-17 09:08:14

76

Views

Positive definiteness of a matrix-valued function

Published on 17 Mar 2023 - 9:08

score 126 · Answer 13 · 2026-03-27 13:47:13

126

Views

Singular matrix, non-vanishing principal minors

Published on 27 Mar 2026 - 13:47

score 116 · Answer 14 · 2023-03-24 17:17:33

116

Views

Does $\frac{1}{2}B^{1/2} \preceq A \preceq B^{1/2}$ imply $AB^{-1}A\preceq \text{constant}\cdot I$?

Published on 24 Mar 2023 - 17:17

score 124 · Answer 15 · 2023-03-28 11:46:43

124

Views

$A+B+\frac{1}{2}BA^{-1}B$ is positive definite.

Published on 28 Mar 2023 - 11:46

List Question

Positivity of a matrix built on Pascal's triangle

An interesting property of positive definite and essentially non-negative matrix

If $A=B+C$, $A,B,C$ are semipositive definite matrices, prove that $\text{im}A=\text{im}B+\text{im}C$

Can we show the block matrix of the inverse of $A$ is greater than the inverse of the block matrix of $A$?

Is the symmetric matrix $vv^{T} - hI$ is strictly negative definite for all small enough $h>0$? Is $\det(vv^{T} - hI)<0$ for small positive $h?$

When is the inverse of a sparse SPD matrix also sparse?

If X is a symmetric diagonal dominant PD matrix, C and K are diagonal positive matrices. Can I find some bounds on C, K to make K(CX +I) PD?

Suppose A is a nonsymmetric PD matrix. K is a diagonal matrix, with all entries nonnegative, Can I find a bound of K such that $A^TA+KA+AK$ is PD?

Solving a quadratic program with simple linear constraints

Are these conditions sufficient to guarantee positive definiteness?

minima function is positive defined

Positive definiteness of a matrix-valued function

Singular matrix, non-vanishing principal minors

Does $\frac{1}{2}B^{1/2} \preceq A \preceq B^{1/2}$ imply $AB^{-1}A\preceq \text{constant}\cdot I$?

$A+B+\frac{1}{2}BA^{-1}B$ is positive definite.

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