Please help me to finish these 7 problems. Let V be a complex inner product spac
ID: 2984304 • Letter: P
Question
Please help me to finish these 7 problems.
Let V be a complex inner product space and prove that T L(V) is invertible if and only if T* is invertible. Give an example an operator T L(C2) which is not self adjoint but there is a lambda C for which lambda T is self adjoint. Show that T(x, y) = (x + y, x - y) is normal and find a basis for C2 for which M(T, B) is diagonal. Find the change of basis matrix to (convert) the standard basis for C3 to the basis {(1, 1, 1), (0, 1, -1), (1,1,0)}. Find the characteristic polynomial for the operator T C3 given by T(x, y, z) = (x - y + z, x, y + z). Use the characteristic polynomial to determine the eigenvalues and the trace of the operator. Let A and B be n times n matrices and prove that if AB = I then BA = I. Let V be a complex inner product space. Prove that = trace (ST*) defines an inner product on L(V).Explanation / Answer
post the 7 problems please