Recall that any complex number 2 can be written in polar form 2 = new where r = |z| is a nonnegative real number and |ei9| = 1. This breaks a complex number down into a stretching factor r and a rotation factor em. There is also a similar representation for linear transformations and matrices. Consider the matrix A e Fm\". A. polar decomposition of A consists of a unitary matrix U and positive semidefinite matrix B such that A = BU. Suppose that A = QEP'\" is a singular value decomposition of A. Show that setting 8 = 020* and U = QP'\" yields a polar decomposition of A (Le, demonstrate that B is positive semidefinite and U is unitary}. Note. While we focus here on square matrices, it turns out any matrix or linear transformation has a polar decomposition (with a slightly modified definition)! If you are interested, you can find more detail in Section 7.6 in the textbook