Let A = xyT, where x ∈ Rm, y ∈ Rn, and both x and y are nonzero vectors. Show that A has a singular value decomposition of the form H1∑H2, where H1 and H2 are Householder transformations and
σ1 = ||x|| ||y||, σ2 = σ3 = . . . = σn = 0