A negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive.
A matrix 
may be tested to determine if it is negative semidefinite in the Wolfram
Language using NegativeSemidefiniteMatrixQ[m].
Negative Semidefinite Matrix
See also
Negative Definite Matrix, Positive Definite Matrix, Positive Semidefinite MatrixExplore with Wolfram|Alpha
References
Marcus, M. and Minc, H. A Survey of Matrix Theory and Matrix Inequalities. New York: Dover, p. 69, 1992.Referenced on Wolfram|Alpha
Negative Semidefinite MatrixCite this as:
Weisstein, Eric W. "Negative Semidefinite Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NegativeSemidefiniteMatrix.html