In a physics book that I have, the author states a very important result but without proving it. He does provide clues for the proof though! It goes like this..(adsbygoogle = window.adsbygoogle || []).push({});

Consider the eigenvalue equation

[tex](M^{-1}K-\omega ^2 I)\vec{v} = \vec{0}[/tex]

where M is an n x n diagonal matrixwhose elements are all positive(first clue) and K is asymetric(second clue) n x n matrix. Then the matrix [itex]M^{-1}K[/itex] has exactly n linearly independant eigenvectors.

Edit: The elements of the K matrix are all positive too!

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

Dismiss Notice

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!

# Clues for the eigenstuff proof

Loading...

Similar Threads for Clues eigenstuff proof |
---|

A Is the proof of these results correct? |

I Doubt about proof on self-adjoint operators. |

I Addition of exponents proof in group theory |

B Help understanding a proof |

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