Inertia of partial transpose of positive semidefinite matrices
Inertia of partial transpose of positive semidefinite matrices
Abstract We show that the partial transpose of <?CDATA $9\times9$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>9</mml:mn> <mml:mo>×</mml:mo> <mml:mn>9</mml:mn> </mml:math> positive semidefinite matrices do not have inertia <?CDATA $(4,1,4)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> and <?CDATA $(3,2,4)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> …