Indefinite Matrix

An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that


where x^* denotes the conjugate transpose.

A matrix m may be tested to see if it is indefinite in the Wolfram Language using IndefiniteMatrixQ[m].

See also

Determinant, Eigenvalue, Hermitian Matrix, Matrix, Negative Definite Matrix, Negative Semidefinite Matrix, Positive Definite Matrix, Positive Eigenvalued Matrix, Positive Semidefinite Matrix

Explore with Wolfram|Alpha


Horn, R. A. and Johnson, C. R. Matrix Analysis, repr. with corr. Cambridge, England: Cambridge University Press, p. 397, 1987.

Referenced on Wolfram|Alpha

Indefinite Matrix

Cite this as:

Weisstein, Eric W. "Indefinite Matrix." From MathWorld--A Wolfram Web Resource.

Subject classifications