# Eigenvalues of n x n matrix

#### coldstone

Just wondering is there a way to get the characteristic equation of an n by n matrix without going through tedious calculations of solving multiple determinants of matrices?

Related Calculus and Beyond Homework Help News on Phys.org

#### Quantumpencil

I think you're basically stuck using the determinant, but there are many ways to simplify a matrix so that calculating it's determinant is easier.

#### lurflurf

Homework Helper
There are many ways
-Hamiltan-Cayley
Find powers of the matrix and find the polynomial they satisfy
-eigenvalues
The terms of the characteristic polynomial are home geneous combinations of the eigenvalues
p=(x-eigenvalue1)(x-eigenvalue2)(x-eigenvalue3)...

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving