Definite Matirx

Definite matrix

Definition

Positive-definite matrix

In mathematics, a symmetric matrix M with real entries is positive-definite if the real number \(z^TMz\)is positive for every nonzero real column vector \(z\), A Hermitian matrix(a complex matrix equal to its conjugate transpose is positive-definite if the real number \(z^{*}Mz\) is positive

Positive semi-definite

Defined similarly, except that \(z^TMz\) and \(z^{*}Mz\) are required to be positive or zero. Negative-definite and negative semi-definite matrices are defined are defined analogously. A matrix that is not positive seme-definite are not negative semi-definite is sometimes called indefinite