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This may be a noob question but I recently read a definition that an inner product on a complex vector space is said to be a positive-definite sesquilinear map.
Doesn't positive definite mean that the inner product will only return positive values?
(Just started studying Functional Analysis specifically Hilbert Spaces)
asked Mar 10, 2015 at 18:46
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Positive-definite in this sense only means that $\langle x, x\rangle > 0$ if $x \neq 0$, it doesn't prohibit general $\langle x, y \rangle$ from being zero, negative, complex, etc.
answered Mar 10, 2015 at 18:47
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