1. ## eigenvalues

if A is a singular matrix, must 0 be an eigenvalue of A?

my logic relied on the fact that the determinant of a singular matrix = 0... is this correct?

2. Originally Posted by ktcyper03
if A is a singular matrix, must 0 be an eigenvalue of A?

my logic relied on the fact that the determinant of a singular matrix = 0... is this correct?

Yes to your question, though your logic works if you know that the determinant of a square matrix is $\pm$ the free coefficient if the matrix's characteristic polynomial...

Tonio

3. Originally Posted by tonio
Yes to your question, though your logic works if you know that the determinant of a square matrix is $\pm$ the free coefficient if the matrix's characteristic polynomial...

Tonio
Or if you know that the determinant of any matrix is just the product of all of its eigenvalues.