I have a system that ideally creates a real symmetric negative definite matrix. However, due to the implementation of the algorithm and/or finite-precision of floating point, the matrix comes out indefinite. For example, in a 2700 square matrix, four eigenvalues are positive, the rest are negative. This is a problem because I want to solve a generalized eigenvalue problem and the fact that neither of my matrices are definite forces me to use very inefficient methods. If it was just a simple eigenvalue problem then I could just do a simple shift, but I need to solve for the problem(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mathbf{A}\mathbf{x}=\lambda\mathbf{B}\mathbf{x}[/tex]

A is real symmetric indefinite and B should be real symmetric negative definite but limitations seem to push it to indefinite. I know I could do matrix multiplication by the transpose of the matrices but then B gets pushed to semi-definite which still is not valid for these methods (Looking at Lanczos which uses Cholesky decomposition on B if it is Hermitian definite).

Does anyone know of a way I could regularize B into a definite matrix without compromising the original eigenvalue problem?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Symmetric definite matrix is being pushed to indefinite in generalized eigen problem.

**Physics Forums | Science Articles, Homework Help, Discussion**