Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I know that for a hermitian matrix to be PSD it is necessary that every principal minor [i.e, the minors obtained by deleting all the last i rows and columns for all i=(n-1)(-1)0].

I want to know if it is necessary that all minors of order>=2 be non-negative.

Particularly, for the 4x4 hermitian matrix

a_11 a_12 a_13 a_14

a_21 a_22 a_23 a_24 (please read it as a matrix)

a_31 a_32 a_33 a_34

a_41 a_42 a_43 a_44

is it necessary that the minors

a_11 a_13

a_31 a_33

and

a_22 a_24

a_42 a_44

should be non-negative?

Please help.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Condition on minors to be Positive Semidefinite (PSD)

Loading...

Similar Threads for Condition minors Positive | Date |
---|---|

A Reality conditions on representations of classical groups | Jan 29, 2018 |

I Linear Algebra Conditions | Feb 15, 2017 |

I Difference Equation Boundary Conditions0. | Oct 10, 2016 |

Condition on Leading principle minors of a symmetric Positive semidefinite(PSD) matri | Apr 4, 2010 |

A condition on principle minors of a symmetric Positive semidefinite (PSD) matrix | Apr 3, 2010 |

**Physics Forums - The Fusion of Science and Community**