Hello~ I've been trying to understand where this orthogonality comes from but I haven't determined a solution. I was wondering if someone could shed some light on this problem. Basically, given(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

{\bf Ax}_n=\lambda_n{\bf Bx}_n \\

{\bf v}=\sum_nc_n{\bf x}_n

[/tex]

when is the following true:

[tex]

c_n=\frac{{\bf x}_n^T{\bf Bv}}{{\bf x}_n^T{\bf Bx}_n}

[/tex]

and why. In my particular problem, I believe [itex]{\bf A}[/itex] is singular and hermitian. I've also read that [itex]{\bf B}[/itex] may have to be positive definite for this orthogonality to occur. I'd be happy if both singular and non-singular cases are addressed.

Thanks :)

Edit:

The orthogonality is

[tex]

\frac{{\bf x}_i^T{\bf Bx}_j}{{\bf x}_i^T{\bf Bx}_i}=\delta_{i,j}

[/tex]

**Physics Forums - The Fusion of Science and Community**

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

# Hermitian General Eigenvalue Problem

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Hermitian General Eigenvalue | Date |
---|---|

A Hilbert-adjoint operator vs self-adjoint operator | Jan 24, 2018 |

I Non-Hermitian wavefunctions and their solutions | Jan 18, 2018 |

A What separates Hilbert space from other spaces? | Jan 15, 2018 |

I From Non Hermitian to Hermitian Matrix | Nov 8, 2016 |

**Physics Forums - The Fusion of Science and Community**