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  1. B

    Complex matrix problem

    I honorstly don't know... I don't think the fact that two matrices P and Q sum up to a diagonalmatrix D implies that they are diagonalmatrices themselves - it just means that their non-diagonal elements cancel - as you say yourself... Or what?
  2. B

    Complex matrix problem

    Let A and B be Hermitian matrices with AB = BA and let N = A + iB. 1) Show that N is normal. 2) Show that A = 1/2(N+N*) (* = conjugate transpose) and find a formula for B. 3) Let U be a unitary matrix such that U*NU is a diagonal matrix. Show that U*AU and U*BU is diagonal matrices...
  3. B

    Vector space proof

    how do you prove that if v is an element of V (a vector space), and if r is a scalar and if rv = 0, then either r = 0 or v = 0... it seems obvious, but i have no idea how to prove it...