Suppose that A is a square matrix and it has two distinct eigenvalues, lamda 1 and lamda 2. and that dim(E_lamda1)=n-1. Prove that A is diagonalizable.

GIVEN INFORMATION:

A is a square matrix ( n x n ).

A has two distinct eigenvalues, and .

Proof:

For ann x nmatrix, the dimensions of the eigenspaces must add up tonfor the matrix to be diagonalizable. We are given . Furthermore, we know that and . Thus, .

So, finally, . We have proven that A is diagonalizable.

-Andy