test_solve.py  a x = y 
a=
[[ 0.5         0.33333333  0.25        0.2       ]
 [ 0.33333333  0.25        0.2         0.16666667]
 [ 0.25        0.2         0.16666667  0.14285714]
 [ 0.2         0.16666667  0.14285714  0.125     ]]
y=
[1 2 3 4]
solve x=
[ -380.  3240. -7140.  4480.]
eig d=
[  9.77556281e-01   6.22678235e-02   1.82125544e-03   2.13065856e-05]
eig v=
[[ 0.69524173  0.66277303  0.2722824  -0.05686079]
 [ 0.50244805 -0.18857925 -0.7387851   0.40765231]
 [ 0.395998   -0.4630991  -0.04915549 -0.79139658]
 [ 0.32767436 -0.55741278  0.61452633  0.45197113]]
qr q1=
[[-0.73433307  0.63004604 -0.24700194 -0.05279177]
 [-0.48955538 -0.24889223  0.7359491   0.39593827]
 [-0.36716653 -0.48768449  0.01685578 -0.79187654]
 [-0.29373323 -0.5506891  -0.63014669  0.46192798]]
qr q2=
[[ -6.80889941e-01  -4.89555380e-01  -3.84650655e-01  -3.17628193e-01]
 [  0.00000000e+00  -4.15261261e-02  -5.22175562e-02  -5.39781810e-02]
 [  0.00000000e+00   0.00000000e+00  -1.77232615e-03  -3.10257409e-03]
 [  0.00000000e+00   0.00000000e+00   0.00000000e+00   4.71355083e-05]]
svd s1=
[[-0.69524173  0.66277303 -0.2722824  -0.05686079]
 [-0.50244805 -0.18857925  0.7387851   0.40765231]
 [-0.395998   -0.4630991   0.04915549 -0.79139658]
 [-0.32767436 -0.55741278 -0.61452633  0.45197113]]
svd s2=
[  9.77556281e-01   6.22678235e-02   1.82125544e-03   2.13065856e-05]
svd s3=
[[-0.69524173 -0.50244805 -0.395998   -0.32767436]
 [ 0.66277303 -0.18857925 -0.4630991  -0.55741278]
 [-0.2722824   0.7387851   0.04915549 -0.61452633]
 [-0.05686079  0.40765231 -0.79139658  0.45197113]]
rand(3,3)
[[ 0.15045439  0.49823354  0.47630334]
 [ 0.50705046  0.16318918  0.25259694]
 [ 0.35634222  0.50156971  0.96162452]]
a[0][0]
0.5
a[1][1]
0.25
a[2][2]
0.166666666667
a[3][3]
0.125
a[0][3]
0.2
dir(numpy.linalg)
['LinAlgError', '__builtins__', '__doc__', '__file__', '__name__', '__path__', 'cholesky', 'det', 'eig', 'eigh', 'eigvals', 'eigvalsh', 'info', 'inv', 'lapack_lite', 'linalg', 'lstsq', 'norm', 'pinv', 'qr', 'solve', 'svd', 'tensorinv', 'tensorsolve', 'test']
dir(numpy.matlib)