A negative definite matrix is a Hermitian matrix all of whose eigenvalues are negative.
A matrix 
may be tested to determine if it is negative definite in the Wolfram
Language using NegativeDefiniteMatrixQ[m].
Negative Definite Matrix
See also
Negative Semidefinite 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 Definite MatrixCite this as:
Weisstein, Eric W. "Negative Definite Matrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NegativeDefiniteMatrix.html