*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **F n and A is the matrix of T in this ordered basis, show that det A = c . (d) What is a reasonable name for the scalar c 6 If A is n n over C for odd n , and A T =-A , i.e. A is skew symmetric, then show det A = 0. 6 If A is orthogonal show det A = 1. 6 Let A be n n over C and suppose that it is unitary, i.e. AA * = I n . Show that | det( A ) | = 1. 6 Let A F n n . Prove that there are at most n distinct scalars c in F such that det( cI-A ) = 0 . 6 Let A and B be n n over F . Show that if A is invertible there are at most n scalars c such that cA + B is not invertible. 1...

View
Full
Document