octave:2> w=rand(4,1) w = 0.32649 0.73664 0.13747 0.46356 octave:3> w(1)=0 w = 0.00000 0.73664 0.13747 0.46356 octave:4> eye(4)-2*w*w'/norm(w)^2 ans = 1.00000 0.00000 0.00000 0.00000 0.00000 -0.39780 -0.26085 -0.87961 0.00000 -0.26085 0.95132 -0.16415 0.00000 -0.87961 -0.16415 0.44648 octave:5> -2*w*w'/norm(w)^2 ans = 0.00000 0.00000 0.00000 0.00000 0.00000 -1.39780 -0.26085 -0.87961 0.00000 -0.26085 -0.04868 -0.16415 0.00000 -0.87961 -0.16415 -0.55352 octave:6> Qw=eye(4)-2*w*w'/norm(w)^2 Qw = 1.00000 0.00000 0.00000 0.00000 0.00000 -0.39780 -0.26085 -0.87961 0.00000 -0.26085 0.95132 -0.16415 0.00000 -0.87961 -0.16415 0.44648 octave:7> A=rand(4) A = 0.599966 0.692493 0.201601 0.792700 0.242917 0.235104 0.746525 0.118332 0.352703 0.180886 0.891749 0.624202 0.397654 0.643185 0.294147 0.052919 octave:8> A*Qw ans = 0.599966 -1.025327 -0.118969 -0.288296 0.242917 -0.392341 0.629434 -0.276508 0.352703 -0.853622 0.698694 -0.026798 0.397654 -0.379134 0.103367 -0.590409 octave:9> w(2)=0 w = 0.00000 0.00000 0.13747 0.46356 octave:10> Qw=eye(4)-2*w*w'/norm(w)^2 Qw = 1.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.83833 -0.54516 0.00000 0.00000 -0.54516 -0.83833 octave:11> A A = 0.599966 0.692493 0.201601 0.792700 0.242917 0.235104 0.746525 0.118332 0.352703 0.180886 0.891749 0.624202 0.397654 0.643185 0.294147 0.052919 octave:12> A(3,1) ans = 0.35270 octave:13> A(3,1)=0 A = 0.59997 0.69249 0.20160 0.79270 0.24292 0.23510 0.74652 0.11833 0.00000 0.18089 0.89175 0.62420 0.39765 0.64319 0.29415 0.05292 octave:14> A(4,1)=0 A = 0.59997 0.69249 0.20160 0.79270 0.24292 0.23510 0.74652 0.11833 0.00000 0.18089 0.89175 0.62420 0.00000 0.64319 0.29415 0.05292 octave:15> Qw*A ans = 0.59997 0.69249 0.20160 0.79270 0.24292 0.23510 0.74652 0.11833 0.00000 -0.19900 0.58723 0.49444 0.00000 -0.63782 -0.73274 -0.38465 octave:16> pwd ans = /home/accounts/altri/caliari/aa0809/calcolo_numerico/autovalori octave:17> A=rand(10) A = Columns 1 through 6: 0.337315 0.735175 0.914900 0.089210 0.515353 0.570098 0.062434 0.860182 0.749179 0.068128 0.375675 0.330315 0.031630 0.197811 0.609467 0.656727 0.357578 0.591595 0.306043 0.061244 0.151545 0.579179 0.462262 0.220256 0.822270 0.375123 0.829740 0.414670 0.868955 0.823163 0.361042 0.226600 0.728160 0.153094 0.584571 0.576741 0.552189 0.894366 0.249336 0.826705 0.251275 0.829473 0.488143 0.615771 0.309197 0.020928 0.125594 0.696731 0.062303 0.429021 0.456297 0.872800 0.650231 0.580423 0.445844 0.482052 0.369281 0.281182 0.413993 0.928341 Columns 7 through 10: 0.130393 0.436784 0.414626 0.248592 0.305076 0.816338 0.441745 0.378246 0.041399 0.209846 0.300943 0.636186 0.943583 0.984003 0.185998 0.029471 0.217728 0.900620 0.066815 0.220742 0.616188 0.648604 0.762147 0.145454 0.932846 0.317946 0.503601 0.351129 0.606286 0.679336 0.854717 0.350275 0.908813 0.839131 0.403625 0.065515 0.357075 0.878565 0.260252 0.780309 octave:18> A=rand(6) A = 0.3030860 0.6280826 0.4845226 0.4063409 0.9492911 0.2652365 0.2499634 0.6926468 0.1699022 0.5453164 0.8263270 0.7719785 0.9367381 0.8201810 0.2702097 0.3551151 0.6599147 0.2576931 0.2319933 0.6818330 0.0053743 0.9116102 0.8978328 0.9991464 0.3544065 0.1873438 0.6195433 0.4079231 0.0074164 0.5456885 0.0358691 0.9464319 0.1909153 0.7859780 0.7427781 0.7424754 octave:19> householder(A) warning: time stamp for `/home/accounts/altri/caliari/aa0809/calcolo_numerico/autovalori/householder.m' is in the future A = 0.30309 -0.99288 -0.67584 0.11897 0.51028 0.22080 -1.05862 1.24595 1.20904 -0.38412 -0.35903 -0.77189 0.00000 0.67865 0.62923 -0.40552 -0.33421 -0.86221 0.00000 -0.34856 -0.61822 0.54677 0.38206 0.69451 0.00000 -0.16599 0.54077 0.06699 -0.44990 0.11377 0.00000 -0.78415 -1.03028 0.45100 0.23748 0.65230 A = 0.30309 -0.99288 0.68497 -0.14672 0.38375 -0.37692 -1.05862 1.24595 -1.46333 0.13764 -0.11055 0.40193 0.00000 -1.10657 1.92383 0.13489 0.13291 -0.15827 0.00000 0.00000 0.49585 0.17439 0.16377 -0.04330 0.00000 0.00000 -0.58553 0.21315 -0.39980 0.49016 0.00000 0.00000 -0.08924 -0.08112 -0.10807 -0.32001 A = 0.30309 -0.99288 0.68497 0.34153 0.15834 -0.41127 -1.05862 1.24595 -1.46333 -0.12572 0.01104 0.42046 0.00000 -1.10657 1.92383 -0.00413 0.19708 -0.14848 0.00000 0.00000 -0.77244 -0.30284 -0.26227 0.38652 0.00000 0.00000 0.00000 -0.24012 0.10786 0.33912 0.00000 0.00000 0.00000 -0.04500 -0.07927 -0.35044 A = 0.30309 -0.99288 0.68497 0.34153 -0.07988 -0.43340 -1.05862 1.24595 -1.46333 -0.12572 -0.08829 0.41123 0.00000 -1.10657 1.92383 -0.00413 -0.16636 -0.18225 0.00000 0.00000 -0.77244 -0.30284 0.18659 0.42821 0.00000 0.00000 0.00000 0.24430 0.13936 -0.24734 0.00000 0.00000 0.00000 0.00000 0.17105 -0.38193 ans = 0.30309 -0.99288 0.68497 0.34153 -0.07988 -0.43340 -1.05862 1.24595 -1.46333 -0.12572 -0.08829 0.41123 0.00000 -1.10657 1.92383 -0.00413 -0.16636 -0.18225 0.00000 0.00000 -0.77244 -0.30284 0.18659 0.42821 0.00000 0.00000 0.00000 0.24430 0.13936 -0.24734 0.00000 0.00000 0.00000 0.00000 0.17105 -0.38193 octave:20> quit