Linear matrix inequalities and control theory/pages/Notion of Matrix Positivity: Revision history

6 December 2021

• curprev 21:4921:49, 6 December 2021 imported>Margav06 1,595 bytes +1,595 Created page with "== '''Notation of Positivity''' == A symmetric matrix <math>A\in\R^{n\times n}</math> is defined to be: '''positive semidefinite''', <math>(A\ge 0)</math>, if <math>x^TAx\ge 0 </math> for all <math>x\in\R^n, x\neq \mathbf{0} </math>. '''positive definite''', <math>(A>0)</math>, if <math>x^TAx> 0 </math> for all <math>x\in\R^n, x\neq \mathbf{0} </math>. '''negative semidefinite''', <math>(-A\ge 0)</math>. '''negative definite''', <math>(-A>0)</math>. '''indefinite..."