Thread: nonpositive matrix

What is a nonpositive matrix?

Originally Posted by Ene Dene

What is a nonpositive matrix?

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I assume it is a matrix whose entries are all negative or zeros. Then you can "factor" a negative from a matrix because of the scaler multiple rule, thus transforming it into a nonnegative matrix.

I agree with the previous response.
The classical definition of a matrix being negative semidefinite is that none of its entries are positive. That is just another way of saying its entries are all non-positive.

Originally Posted by Ene Dene

What is a nonpositive matrix?

A Negative Definite Matrix - A Hermitian matrix all of whose eigenvalues are
negative (or one of the equivalent definitions).

A Negative Semi-Definite Matrix - A Hermitian matrix all of whose eigenvalues
are <=0 (or one of the equivalent definitions).

RonL