Thread: Matrix eigenvalues

If you are told that a square matrix M is diagonalisable, and it has only one eigenvalue which is c, then how do you show that M=cI, where I is the identity matrix?

Alternatively, and more generally, can you say that the sum of the eigenvalues of a diagonalisable square matrix M is the sum of the values along the main diagonal of M? How would you prove that?

See here:

http://www.mathhelpforum.com/math-he...ues-proof.html

I think I understand the second part. What about the 1st part?

Originally Posted by GrassyRoots

I think I understand the second part. What about the 1st part?

Proof: Applying the definition of diagonalizability: M is diagble invertible P such that . Since all its eigen values are c, . But . Thus