Positive-definite matrix

In linear algebra, a symmetric n × n real matrix $M$ is said to be positive definite if the scalar $z^{\mathrm{T}}Mz$ is positive for every non-zero column vector $z$ of $n$ real numbers. Here $z^{\mathrm{T}}$ denotes the transpose of $z$ .

More generally, an n × n Hermitian matrix $M$ is said to be positive definite if the scalar $z^{*}Mz$ is real and positive for all non-zero column vectors $z$ of $n$ complex numbers. Here $z^{*}$ denotes the conjugate transpose of $z$ .

单词	Nonnegative definite
释义	Nonnegative definite 英语百科 Positive-definite matrix In linear algebra, a symmetric n × n real matrix $M$ is said to be positive definite if the scalar $z^{\mathrm{T}}Mz$ is positive for every non-zero column vector $z$ of $n$ real numbers. Here $z^{\mathrm{T}}$ denotes the transpose of $z$ . More generally, an n × n Hermitian matrix $M$ is said to be positive definite if the scalar $z^{}Mz$ is real and positive for all non-zero column vectors $z$ of $n$ complex numbers. Here $z^{}$ denotes the conjugate transpose of $z$ .
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Nonnegative definite

Positive-definite matrix