Inverse matrix in Matlab very different to Excel

Replicating calculations carried out in Excel in Matlab in order to learn. Inverting the matrix below gave a very different answer in Matlab to excel.

Original Matrix:

1322252    0	        2010	-1006
0	    1322252	1006	2010
2010	    1006	4	0
-1006	    2010	0	4

Inverted Matrix using inv(matrix)

      1.68867574048431e-05       5.0821976835258e-21      -0.00848559559593365       0.00424701948731803
       5.0821976835258e-21      1.68867574048431e-05      -0.00424701948731803      -0.00848559559593364
      -0.00848559559593365      -0.00424701948731803          5.58213718801715     -1.28379263845227e-15
       0.00424701948731803      -0.00848559559593364     -1.28379263845227e-15          5.58213718801714

Inverted Matrix using Excel

               1.68868e-05              -1.34343e-20              -0.008485596               0.004247019
               2.82121e-20               1.68868e-05              -0.004247019              -0.008485596
              -0.008485596              -0.004247019               5.582137188              -6.91897e-15
               0.004247019              -0.008485596               6.91897e-15               5.582137188

Inverting the below matrix did work as expected (same answer in Excel and Matlab)

               419	163	1	0
               -163	419	0	1
                586	340	1	0
                -340	586	0	1

[Jeremy]

This is probably a case of different methods and/or numerical tolerances. The results are approximately the same, 5.0821976835258e-21 and -1.34343e-20 are both essentially zero

Answer 1

[Fabio Freschi]

The answer is not very different. As Jeremy commented, the results are similar a part from numerical tolerances. You can verify yourself comparing the matrices. In the following I load your matrices (note that excel data have less digits):

A1 = [      1.68867574048431e-05       5.0821976835258e-21      -0.00848559559593365       0.00424701948731803
       5.0821976835258e-21      1.68867574048431e-05      -0.00424701948731803      -0.00848559559593364
      -0.00848559559593365      -0.00424701948731803          5.58213718801715     -1.28379263845227e-15
       0.00424701948731803      -0.00848559559593364     -1.28379263845227e-15          5.58213718801714];
A2 = [               1.68868e-05              -1.34343e-20              -0.008485596               0.004247019
               2.82121e-20               1.68868e-05              -0.004247019              -0.008485596
              -0.008485596              -0.004247019               5.582137188              -6.91897e-15
               0.004247019              -0.008485596               6.91897e-15               5.582137188];

Then you can compare the two matrices entry-by-entry:

A1-A2

ans =

  -4.2595e-11   1.8516e-20   4.0407e-10   4.8732e-10
  -2.3130e-20  -4.2595e-11  -4.8732e-10   4.0407e-10
   4.0407e-10  -4.8732e-10   1.7150e-11   5.6352e-15
   4.8732e-10   4.0407e-10  -8.2028e-15   1.7140e-11

And you can see the errors are "small" in absolute value (the largest difference is at the 10th digit)

As a global index you can use the (relative) norm of the matrices

norm(A1-A2)/norm(A1)

ans =

   1.1581e-10

[Rosie G]

Thank you so much for your fast reply, and I feel very foolish now!

[Fabio Freschi]

No problem, sometimes obvious things slip under the radar!