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negative definite (Definition)

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

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

we call $A$ a negative definite matrix.



"negative definite" is owned by drini. [ owner history (1) ]
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See Also: positive definite, positive semidefinite, quadratic form
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Cross-references: matrix, non-zero vector, square matrix, real, symmetric
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This is version 1 of negative definite, born on 2002-02-15, modified 2002-02-15.
Object id is 1968, canonical name is NegativeDefinite.
Accessed 6628 times total.

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