Vipul: Created page with "{{real square matrix property}} ==Definition== Suppose $n$ is a positive integer and $A$ is a $n \times n$ square matrix. We say that $..."$

2014-05-01T16:52:51Z

Created page with "{{real square matrix property}} ==Definition== Suppose <math>n</math> is a positive integer and <math>A</math> is a <math>n \times n</math> square matrix. We say that <math>..."

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{{real square matrix property}}

==Definition==

Suppose <math>n</math> is a positive integer and <math>A</math> is a <math>n \times n</math> square matrix. We say that <math>A</math> is a '''P-matrix''' if all the [[principal minor]]s of <math>A</math> are positive.

==Relation with other properties==

===Stronger properties===

{| class="sortable" border="1"
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
|-
| [[Weaker than::symmetric positive-definite matrix]] || || || || {{intermediate notions short|P-matrix|symmetric positive-definite matrix}}
|-
| [[Weaker than::positive-definite matrix]] || || || || {{intermediate notions short|P-matrix|positive-definite matrix}}
|-
| [[Weaker than::nonsingular M-matrix]] || || || || {{intermediate notions short|P-matrix|nonsingular M-matrix}}
|}

P-matrix - Revision history

Vipul: Created page with "{{real square matrix property}} ==Definition== Suppose n is a positive integer and A is a n \times n square matrix. We say that ..."

Vipul: Created page with "{{real square matrix property}} ==Definition== Suppose $n$ is a positive integer and $A$ is a $n \times n$ square matrix. We say that $..."$