PlanetMath: positive semidefinite

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positive semidefinite

(Definition)

Let be an $n\times n$ symmetric real square matrix. If for any non-zero vector we have

$\begin{displaymath}x^t Ax\geq 0,\end{displaymath}$

we call

a positive semidefinite matrix.

"positive semidefinite" is owned by drini. [ owner history (1) ]

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Cross-references: matrix, non-zero vector, square matrix, real, symmetric
There are 11 references to this entry.

This is version 2 of positive semidefinite, born on 2002-02-15, modified 2002-02-15.
Object id is 1969, canonical name is PositiveSemidefinite.
Accessed 10087 times total.

Classification:

15A48 (Linear and multilinear algebra; matrix theory :: Positive matrices and their generalizations; cones of matrices)

Pending Errata and Addenda

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