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# positive definite form

A bilinear form $B$ on a real or complex vector space $V$ is positive definite if $B(x,x)>0$ for all nonzero vectors $x\in V$. On the other hand, if $B(x,x)<0$ for all nonzero vectors $x\in V$, then we say $B$ is negative definite. If $B(x,x)\geq 0$ for all vectors $x\in V$, then we say $B$ is nonnegative definite. Likewise, if $B(x,x)\leq 0$ for all vectors $x\in V$, then we say $B$ is nonpositive definite.

A form which is neither positive definite nor negative definite is called indefinite.

Synonym:

positive definite, negative definite form, negative definite, indefinite form, indefinite, nonnegative definite, nonpositive definite

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Definition

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Reference

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## Mathematics Subject Classification

11E39*no label found*15A63

*no label found*47A07

*no label found*

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## Comments

## Positive definite vs positve definite form

There seem to be two entries, one for "positive definite" the other for "positve definite form"; they don't seem to reference each other.