Positive semi-definite matrix

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

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