Definite matrix: Difference between revisions

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== Generalizations ==

Suppose <math>K</math> denotes the [[field (mathematics)|field]] <math>\mathbb{R}</math> or <math>\mathbb{C}</math>, <math>V</math> is a [[vector space]] over <math>K</math>, and <math>B : V \times V \rightarrow K</math> is a [[bilinear]] map which is Hermitian in the sense that <math>B(x, y)</math> is always the complex conjugate of <math>B(y, x)</math>.

Then <math>B</math> is called ''positive definite'' if <math>B(x, x) > 0</math> for every nonzero <math>x</math> in <math>V</math>.