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Linear Algebra

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Moderate

Meaning of Positive Definite

LINALG-VGV1WP

Which of the following statements is equivalent to the statement that “the bilinear form $\langle-,-\rangle$ on the vector space $V$ is positive definite”?

A

$\langle v,w\rangle>0$ for all vectors $v,w\in V$

B

$\langle v,w\rangle\geq0$ for all vectors $v,w\in V$

C

$\langle v,w\rangle>0$ for all nonzero vectors $v,w\in V$

D

$\langle v,v\rangle\geq0$ for all vectors $v\in V$

E

$\langle v,v\rangle>0$ for all nonzero vectors $v\in V$