Question

why do the matrices AAT and ATA have the same characteristic polynomial?

Answer 1

what is* AAT and ATA

Answer 2

matrix A multiplied by its transpose

Answer 3

in both directions

Answer 4

a transpose does not effect the diagonal ...

Answer 5

but that may just be a spurious thought that has nothing to do with this

Answer 6

remind me how we determine a characteristic poly .... something to do eugene vectors im sure

Answer 7

its the determinant of (A-lambda I).

Answer 8

where lambda is the eigen value and I, the identity matrix

Answer 9

Hint: \(\det(A-\lambda I) = \det(A^T-\lambda I)\). Now what is \((AA^T)^T\)? :-)