Characteristic values of arbitrary matrices

Here the elements a, b, c, d, are~ respectlvely~ in the (il)~ Let us consider the n-d/mensional matrix (lJ), (Jl), and (J j), position of A. This matrix can be re<lucecl to triangular form by-p an infinite series of unitary transformations A ~ T~ A~ T, , T ~ = T ~ • We choose the transform to be of the form T= .(l-PP-" .~ o wlth t ~ (l e). ~u8 ~ con~B t,-(1-r~) ~, ! (l-r2) 2, aacl the co.,plex conjugate t of t in the positions corresponding to a, b, c, ~, unity everywhere else on the-,A~I-d/agonal, and zeros in the remainln6 positions. The number t will be appropriately &etermine& later. with ~ denoting a unit matrix of k dimensions, 0 ~ d.enoting a recta~ular matrix of zeros h~ving r rows and s columas, and, f~n=1~y, S a square matrix of J-i÷l dimensions. Similarly, let us denote the correspondlng parts of ~ C b A = E F H J K