Give examples of
- Two different inner products for P4.
- A 2*2 matrix that is diagonalizable over the complex numbers but not over the real numbers.
- A 4*4 matrix that is not diagonal but is diagonalizable.
- A 3*3 matrix that is not diagonalizable.
- A subspace of P3 of dimension 2 and containing the vector X2-1.
- A non invertible square matrix.
Appreciated for any explaining.