Matches in SemOpenAlex for { <https://semopenalex.org/work/W4304891548> ?p ?o ?g. }
Showing items 1 to 45 of
45
with 100 items per page.
- W4304891548 abstract "Abstract We prove the following Farkas’ Lemma for simultaneously diagonalizable bilinear forms: If $$A_1,ldots ,A_k$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> </mml:math> , and $$B:mathbb {R}^n times mathbb {R}^n rightarrow mathbb {R}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>:</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>→</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> are bilinear forms, then one—and only one—of the following holds: $$B=a_1 A_1 + cdots + a_k A_k,$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> with non-negative $$a_itext {'s}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mtext>'s</mml:mtext> </mml:mrow> </mml:math> , there exists ( x , y ) for which $$A_1(x,y) ge 0 , ldots , A_k(x,y) ge 0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and $$B(x,y) < 0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . We study evaluation maps over the space of bilinear forms and consequently construct examples in which Farkas’ Lemma fails in the bilinear setting." @default.
- W4304891548 created "2022-10-13" @default.
- W4304891548 creator A5005186986 @default.
- W4304891548 creator A5016420430 @default.
- W4304891548 creator A5018770741 @default.
- W4304891548 creator A5035736049 @default.
- W4304891548 date "2022-10-13" @default.
- W4304891548 modified "2023-10-18" @default.
- W4304891548 title "Farkas’ Lemma in the bilinear setting and evaluation functionals" @default.
- W4304891548 cites W1598937922 @default.
- W4304891548 cites W2020563369 @default.
- W4304891548 cites W2057385360 @default.
- W4304891548 cites W2072904618 @default.
- W4304891548 doi "https://doi.org/10.1007/s13398-022-01337-y" @default.
- W4304891548 hasPublicationYear "2022" @default.
- W4304891548 type Work @default.
- W4304891548 citedByCount "0" @default.
- W4304891548 crossrefType "journal-article" @default.
- W4304891548 hasAuthorship W4304891548A5005186986 @default.
- W4304891548 hasAuthorship W4304891548A5016420430 @default.
- W4304891548 hasAuthorship W4304891548A5018770741 @default.
- W4304891548 hasAuthorship W4304891548A5035736049 @default.
- W4304891548 hasBestOaLocation W43048915481 @default.
- W4304891548 hasConcept C11413529 @default.
- W4304891548 hasConcept C41008148 @default.
- W4304891548 hasConceptScore W4304891548C11413529 @default.
- W4304891548 hasConceptScore W4304891548C41008148 @default.
- W4304891548 hasIssue "1" @default.
- W4304891548 hasLocation W43048915481 @default.
- W4304891548 hasOpenAccess W4304891548 @default.
- W4304891548 hasPrimaryLocation W43048915481 @default.
- W4304891548 hasRelatedWork W2051487156 @default.
- W4304891548 hasRelatedWork W2052122378 @default.
- W4304891548 hasRelatedWork W2053286651 @default.
- W4304891548 hasRelatedWork W2073681303 @default.
- W4304891548 hasRelatedWork W2317200988 @default.
- W4304891548 hasRelatedWork W2544423928 @default.
- W4304891548 hasRelatedWork W2947381795 @default.
- W4304891548 hasRelatedWork W2181413294 @default.
- W4304891548 hasRelatedWork W2181743346 @default.
- W4304891548 hasRelatedWork W2187401768 @default.
- W4304891548 hasVolume "117" @default.
- W4304891548 isParatext "false" @default.
- W4304891548 isRetracted "false" @default.
- W4304891548 workType "article" @default.