Singular matrix issue with Numpy

Question

I am trying to multiply a vector 3 by 1  by its transpose 1 by 3   I get a  3 by 3  array but I cannot get its inverse  Any idea why   import numpy as np  c array  1  8  50   np transpose c np newaxis     c array      1     8    50          8    64   400         50   400  2500    np linalg inv np transpose c np newaxis     c  Traceback  most recent call last     File   lt console gt    line 1  in  lt module gt    File  C  Python26 lib site-packages numpy linalg linalg py   line 445  in inv     return wrap solve a  identity a shape 0   dtype a dtype      File  C  Python26 lib site-packages numpy linalg linalg py   line 328  in solve     raise LinAlgError   Singular matrix  LinAlgError  Singular matrix

User · Answer

The matrix you pasted        1     8    50        8    64   400       50   400  2500     Has a determinant of zero  This is the definition of a Singular matrix  one for which an inverse does not exist   http   en wikipedia org wiki Invertible matrix

User · Answer

Use SVD or QR-decomposition to calculate exact solution in real or complex number fields   numpy linalg svd numpy linalg qr

User · Answer

By definition  by multiplying a 1D vector by its transpose  you ve created a singular matrix   Each row is a linear combination of the first row     Notice that the second row is just 8x the first row   Likewise  the third row is 50x the first row   There s only one independent row in your matrix

User · Answer

As it was already mentioned in previous answers  your matrix cannot be inverted  because its determinant is 0   But if you still want to get inverse matrix  you can use np linalg pinv  which leverages SVD to approximate initial matrix

[python] Singular matrix issue with Numpy

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