Hope someone can help me out here.. I've found the eigenvalues (lamda) of this matrix, but through a very very long way, does anyone know of a quicker way (there must be a quicker way). The matrix is 3x3:(adsbygoogle = window.adsbygoogle || []).push({});

H = ( E, a, a; a, E, a; a, a, E ).

I can reduce the determinant to the following, but still troublesome:

det(H) = | E - lamda, a, a; a, E - lamda, a; a, a, E - lamda |

det(H) = | E - lamda - a, a - E + lamda, 0; 0, E - lamda - a, a - E + lamda; a, a, E - lamda |

**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!

# Determinant of this special matrix

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