= Stretches. In analogy with the polar decomposition w = x + iy pe of complex numbers, any matrix A can be decomposed A = RS into a stretch S and a rotation R; the building blocks of all linear operators. Show that two eigenvectors V, Vj of S, with distinct eigenvalues X X, must be orthogonal ( Vj = 0); and, therefore, that the matrix of eigenvectors is an orthogonal transformation (V*V = I). Bonus: Interpret the resulting decompositions S = VWV and W = VSV in terms of rotations. that Calculate the eigenvalues and eigenvectors of M =(1-1). Do they look familiar? Show 1/1 1 - (-) (679) (7) = 2 0 and M eM - = VWVt - (1-4) (8) (17) i i 0 VeWoyt