Definite matrix
Property of a mathematical matrix / From Wikipedia, the free encyclopedia
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In mathematics, a symmetric matrix with real entries is positive-definite if the real number
is positive for every nonzero real column vector
where
is the row vector transpose of
[1]
More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number
is positive for every nonzero complex column vector
where
denotes the conjugate transpose of
Positive semi-definite matrices are defined similarly, except that the scalars and
are required to be positive or zero (that is, not negative). Negative-definite and negative semi-definite matrices are defined analogously. A matrix that is not positive semi-definite and not negative semi-definite is sometimes called indefinite.