## Number of Eigenvalues in a Matrix

**How many eigenvalues are there in a matrix?**

**Equivalent to the roots of the matrix’â„¢s characteristic polynomial.**

The number of eigenvalues of a matrix M can be computed using the formula M??*I*)**v** =?0 v, where *l *is the identity matrix, ? is equal to the number of eigenvalues of the matrix, and v is its corresponding eigenvector. One has to expand the equation into characteristic polynomials of ?, and then get the roots of the characteristic polynomial.

This fact is verified on : March 29, 2010.