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positive definite form
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(Definition)
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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 $B(x,x) \ge 0$ for all vectors $x
\in V$ then we say $B$ is nonnegative definite. Likewise, if $B(x,x) \le 0$ 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.
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"positive definite form" is owned by djao.
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| Other names: |
positive definite, negative definite form, negative definite, indefinite form, indefinite, nonnegative definite, nonpositive definite |
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Cross-references: vectors, vector space, complex, real, bilinear form
There are 27 references to this entry.
This is version 2 of positive definite form, born on 2002-02-22, modified 2004-09-20.
Object id is 2472, canonical name is PositiveDefiniteForm.
Accessed 19432 times total.
Classification:
| AMS MSC: | 11E39 (Number theory :: Forms and linear algebraic groups :: Bilinear and Hermitian forms) | | | 15A63 (Linear and multilinear algebra; matrix theory :: Quadratic and bilinear forms, inner products) | | | 47A07 (Operator theory :: General theory of linear operators :: Forms ) |
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Pending Errata and Addenda
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