# Eigenvalues and Eigenvectors uniquely define a matrix

1. Jul 1, 2009

### zeebo17

Do a set of Eigenvalues and Eigenvectors uniquely define a matrix since you can produce a matrix $$M$$ from a matrix of its eigenvectors as columns $$P$$ and a diagonal matrix of the eigenvalues $$E$$ through $$M=P E P^{\dagger}$$?

2. Jul 1, 2009

### ice109

i'm pretty sure the answer is yes

3. Jul 1, 2009