a matematical problem with matrix inversion

Hi all; i have a simple and stupid problem!! consider u is a non-squared matrix, why the following equation is not equal to Identity matrix when executing in MATLAB:

     U' * inv( U * U') *U

Thanks in advance, Z.Z

Answer 1

[Sean de Wolski]

U = magic(4); %sample data
U = U(:,1:3); %non-square it
U'*(( U * U')\U)  %see what happens:
ans   =
          1  -9.7145e-17   2.0817e-16
 2.0817e-17            1  -1.6653e-16
 1.3878e-17   8.3267e-17            1

the 10^-16 is just an artifact of floating point calculations. For all intensive purposes, the above is a 3x3 identity matrix.

Don't use inv, use '\'.

doc mldivide

Also, this for floating point explanation: FAQ6.1

Answer 2

[Walter Roberson]

See http://www.mathworks.com/matlabcentral/answers/13181-inverse-of-non-square-matrix-pinv-not-working