Details and Options
- A matrix m is indefinite if its Hermitian part is neither a positive nor a negative semidefinite matrix.
- IndefiniteMatrixQ works for symbolic as well as numerical matrices.
- For approximate matrices, the option Tolerance->t can be used to indicate that all eigenvalues λ satisfying λ≤t λmax are taken to be zero where λmax is an eigenvalue largest in magnitude.
- The option Tolerance has Automatic as its default value.
Examplesopen allclose all
Basic Examples (1)
An approximate MachinePrecision real matrix:
An approximate MachinePrecision complex matrix:
The test returns False unless it is true for all possible complex values of symbolic parameters:
Adjust the option Tolerance to give a correct answer:
Properties & Relations (6)
Possible Issues (1)
The function returns False for symbolic matrices having non-numeric eigenvalues that cannot be determined as non-positive or non-negative: