PlanetMath: negative semidefinite

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negative semidefinite

(Definition)

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

$\begin{displaymath}x^t Ax\leq0,\end{displaymath}$

we call

a negative semidefinite matrix.

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

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Cross-references: matrix, non-zero vector, square matrix, real, symmetric
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This is version 1 of negative semidefinite, born on 2002-02-15.
Object id is 1970, canonical name is NegativeSemidefinite.
Accessed 3945 times total.

Classification:

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

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