Positive Semidefinite Matrix

A positive semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonnegative.

A matrix m may be tested to determine if it is positive semidefinite in the Wolfram Language using PositiveSemidefiniteMatrixQ[m].

See also

Negative Definite Matrix, Negative Semidefinite Matrix, Positive Definite Matrix, Positive Eigenvalued Matrix, Positive Matrix

Explore with Wolfram|Alpha


Marcus, M. and Minc, H. Introduction to Linear Algebra. New York: Dover, p. 182, 1988.Marcus, M. and Minc, H. A Survey of Matrix Theory and Matrix Inequalities. New York: Dover, p. 69, 1992.

Referenced on Wolfram|Alpha

Positive Semidefinite Matrix

Cite this as:

Weisstein, Eric W. "Positive Semidefinite Matrix." From MathWorld--A Wolfram Web Resource.

Subject classifications