factors():
  Computing and using matrix factors.

  Compute PLU factorization of A = P * L * U.
  P:
[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]
  L:
[[ 1.          0.          0.          0.        ]
 [ 0.05370206  1.          0.          0.        ]
 [ 0.47009223  0.05383932  1.          0.        ]
 [ 0.91475645 -0.05380217  0.93285297  1.        ]]
  U:
[[ 0.75343358  0.11418889  0.3102412   0.48816003]
 [ 0.          0.85193584  0.11250845  0.5884785 ]
 [ 0.          0.          0.19559601  0.63164206]
 [ 0.          0.          0.         -0.76282031]]
  P * L * U = A?:
[[0.75343358 0.11418889 0.3102412  0.48816003]
 [0.04046094 0.85806801 0.12916904 0.6146937 ]
 [0.35418327 0.09954696 0.34749537 0.89280558]
 [0.68920823 0.05861902 0.46020426 0.24129498]]

  Compute QR factorization A = Q * R.
  Q:
[[-0.69662312  0.01442072  0.63612254 -0.33144589]
 [-0.0374101  -0.99655505  0.01890959  0.07156074]
 [-0.32747712 -0.04691648 -0.69192105 -0.64171866]
 [-0.6372405   0.06684994 -0.34093372  0.68790976]]
  R:
[[-1.08155121 -0.18160079 -0.62801099 -0.80919565]
 [ 0.         -0.85421704 -0.10978879 -0.63129323]
 [ 0.          0.         -0.19754456 -0.37786337]
 [ 0.          0.          0.         -0.52475153]]
  Q * R = A?:
[[0.75343358 0.11418889 0.3102412  0.48816003]
 [0.04046094 0.85806801 0.12916904 0.6146937 ]
 [0.35418327 0.09954696 0.34749537 0.89280558]
 [0.68920823 0.05861902 0.46020426 0.24129498]]

  Compute SVD factorization of A = U * diag ( S ) * V
  U:
[[-0.5314025   0.34580664  0.1908864  -0.74939411]
 [-0.45105374 -0.8162738   0.35922808  0.03468127]
 [-0.57165873 -0.02716529 -0.79781931  0.18961197]
 [-0.43286049  0.46192738  0.44497407  0.63344532]]
  S:
[1.68457836 0.89173256 0.44226206 0.14415462]
  V:
[[-0.54579207 -0.31461629 -0.36862525 -0.68355177]
 [ 0.60136617 -0.71384368  0.22987531 -0.27557808]
 [ 0.41256186  0.62565325  0.07498363 -0.65782078]
 [-0.41262871  0.00134336  0.8975802  -0.15519511]]
  U * diag ( S ) * V = A?:
[[0.75343358 0.11418889 0.3102412  0.48816003]
 [0.04046094 0.85806801 0.12916904 0.6146937 ]
 [0.35418327 0.09954696 0.34749537 0.89280558]
 [0.68920823 0.05861902 0.46020426 0.24129498]]

  Compute eigen factors A*V=V*diag(L)
  L:
[ 1.60035401 -0.36690791  0.21772556  0.74912028]
  V:
[[-0.52178496 -0.04829617 -0.52326031  0.08935044]
 [-0.49968901 -0.23883004 -0.24243486 -0.97621329]
 [-0.51553618 -0.73441564  0.8085253   0.14203584]
 [-0.4607318   0.63345194  0.11709327  0.13729503]]
  A*V
[[-0.83504066  0.01772025 -0.11392714  0.06693423]
 [-0.79967931  0.08762863 -0.05278426 -0.73130118]
 [-0.82504038  0.2694629   0.17603662  0.10640193]
 [-0.73733399 -0.23241853  0.0254942   0.10285049]]
  V*diag(L)
[[-0.83504066  0.01772025 -0.11392714  0.06693423]
 [-0.79967931  0.08762863 -0.05278426 -0.73130118]
 [-0.82504038  0.2694629   0.17603662  0.10640193]
 [-0.73733399 -0.23241853  0.0254942   0.10285049]]