Thread: 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?

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 the free coefficient if the matrix's characteristic polynomial...

Tonio

Originally Posted by tonio

Yes to your question, though your logic works if you know that the determinant of a square matrix is 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.