A positive semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonnegative.
A matrix 
may be tested to determine if it is positive semidefinite in the Wolfram
Language using PositiveSemidefiniteMatrixQ[m].
Positive Semidefinite Matrix
See also
Negative Definite Matrix, Negative Semidefinite Matrix, Positive Definite Matrix, Positive Eigenvalued Matrix, Positive MatrixExplore with Wolfram|Alpha
References
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 MatrixCite this as:
Weisstein, Eric W. "Positive Semidefinite Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PositiveSemidefiniteMatrix.html