Find a unitary matrix U such that UH AU is diagonal, where (: 4 A = -3 2i 0 -2i

2 Consider the matrix A = and the vector u = Let B = (A – A")2 and define vector v = Bu. If v = , write 1 down the value of vị. [Please enter your answer numerically in decimal format.

Let A be an n × n matrix over C, then det(A¯) = det(A), where A¯i,j = Ai,j .Here, z¯ = a − ib when z = a + ib, the complex conjugate of z.

The Hilbert matrix Hn is the n X n matrix [hij], where hij = 1/(i + j — 1). Prove that the matrix H, is symmetric.