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{{Short description|Property of a mathematical matrix}}
{{use dmy dates|date=June 2024}}▼
{{hatnote|Not to be confused with [[Positive matrix]] and [[Totally positive matrix]].}}
▲{{use dmy dates|date=June 2024}}
In [[mathematics]], a symmetric matrix <math>\ M\ </math> with [[real number|real]] entries is '''positive-definite''' if the real number <math>\ \mathbf{x}^\top M \mathbf{x}\ </math> is positive for every nonzero real [[column vector]] <math>\ \mathbf{x}\ ,</math> where <math>\ \mathbf{x}^\top\ </math> is the [[row vector]] [[transpose]] of <math>\ \mathbf{x} ~.</math><ref>
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