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IndefiniteMatrixQ

Test whether a matrix is explicitly indefinite, i.e. whether the Hermitian part of the matrix has both positive and negative eigenvalues.

$ wo 'IndefiniteMatrixQ[{{-1, 0}, {0, 1}}]'
True

A positive definite matrix is not indefinite:

$ wo 'IndefiniteMatrixQ[{{2, 0}, {0, 1}}]'
False