Question

A cone in $\mathbb{R}^n$ containing n linearly independent vectors has a non empty interior

score 359 · Answer 1 · 2019-11-24 11:24:01

359

Views

A cone in $\mathbb{R}^n$ containing n linearly independent vectors has a non empty interior

Published on 24 Nov 2019 - 11:24

score 571 · Answer 2 · 2019-12-10 04:09:19

571

Views

Rewrite as second order cone constraint

Published on 10 Dec 2019 - 4:09

score 155 · Answer 3 · 2026-03-16 20:05:44

155

Views

Does every negative semidefinite matrix lie in the convex cone generated by the squares of skew-symmetric matrices?

Published on 16 Mar 2026 - 20:05

score 481 · Answer 4 · 2026-03-12 21:34:50

481

Views

Is a convex cone which is generated by a closed linear cone always closed?

Published on 12 Mar 2026 - 21:34

score 175 · Answer 5 · 2026-03-14 02:59:17

175

Views

The boundary of the convex hull of squares of skew-symmetric matrices

Published on 14 Mar 2026 - 2:59

score 799 · Answer 6 · 2020-01-17 04:33:48

799

Views

How is a halfspace an affine convex cone?

Published on 17 Jan 2020 - 4:33

score 350 · Answer 7 · 2020-01-21 07:28:08

350

Views

Show sum of two polyhedral cones is a polyhedral cone?

Published on 21 Jan 2020 - 7:28

score 181 · Answer 8 · 2020-01-27 12:40:22

181

Views

Mori cone: extremal ray intersections

Published on 27 Jan 2020 - 12:40

score 506 · Answer 9 · 2020-01-30 21:44:26

506

Views

Is the nonnegative orthant a "convex polyhedral cone"?

Published on 30 Jan 2020 - 21:44

score 121 · Answer 10 · 2020-02-22 01:12:58

121

Views

is a positive ray is a convex cone?

Published on 22 Feb 2020 - 1:12

score 257 · Answer 11 · 2026-03-22 16:03:31

257

Views

Probability that random variable is inside cone

Published on 22 Mar 2026 - 16:03

score 249 · Answer 12 · 2026-03-25 03:22:18

249

Views

Given a closed, convex, full-dimensional cone $K$, how do I show that $u\in int(K) \iff u^tx>0 \quad \forall x\in K^*-\{0\}$?

Published on 25 Mar 2026 - 3:22

score 100 · Answer 13 · 2020-03-05 15:13:48

100

Views

Cone of positive Hilbert-Schmidt operators

Published on 05 Mar 2020 - 15:13

score 94 · Answer 14 · 2026-03-25 03:22:16

94

Views

For full-dimensional cone $K$, $x\in int(K)$, can you take arb. vector $y$ and for some $t$ small enough have that $x-ty\in int(K)$

Published on 25 Mar 2026 - 3:22

score 59 · Answer 15 · 2020-03-08 18:48:02

59

Views

Show that $a^Tz\ge b$ for $z\in K$ if $a^Tz>b$ for $z\in \operatorname{int}(K)$ with $K$ being a convex cone

Published on 08 Mar 2020 - 18:48

List Question

A cone in $\mathbb{R}^n$ containing n linearly independent vectors has a non empty interior

Rewrite as second order cone constraint

Does every negative semidefinite matrix lie in the convex cone generated by the squares of skew-symmetric matrices?

Is a convex cone which is generated by a closed linear cone always closed?

The boundary of the convex hull of squares of skew-symmetric matrices

How is a halfspace an affine convex cone?

Show sum of two polyhedral cones is a polyhedral cone?

Mori cone: extremal ray intersections

Is the nonnegative orthant a "convex polyhedral cone"?

is a positive ray is a convex cone?

Probability that random variable is inside cone

Given a closed, convex, full-dimensional cone $K$, how do I show that $u\in int(K) \iff u^tx>0 \quad \forall x\in K^*-\{0\}$?

Cone of positive Hilbert-Schmidt operators

For full-dimensional cone $K$, $x\in int(K)$, can you take arb. vector $y$ and for some $t$ small enough have that $x-ty\in int(K)$

Show that $a^Tz\ge b$ for $z\in K$ if $a^Tz>b$ for $z\in \operatorname{int}(K)$ with $K$ being a convex cone

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