topic Re: why when i have decimals in the matrix I don't get the exact inverse? in SAS IML in SAS/IML Software and Matrix Computations https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/why-when-i-have-decimals-in-the-matrix-I-don-t-get-the-exact/m-p/683488#M5287 <P><a href="https://communities.sas.com/t5/user/viewprofilepage/user-id/10892">@PaigeMiller</a>&nbsp;is correct. The thing I would add is look at the proc compare documentation for various ways to compare computed numbers. Expecting differences to be zero for nontrivial (or ever some fairly trivial) computations is unrealistic. Also check out:&nbsp;<A href="https://documentation.sas.com/?docsetId=lrcon&amp;docsetTarget=p0ji1unv6thm0dn1gp4t01a1u0g6.htm&amp;docsetVersion=9.4&amp;locale=en" target="_blank">https://documentation.sas.com/?docsetId=lrcon&amp;docsetTarget=p0ji1unv6thm0dn1gp4t01a1u0g6.htm&amp;docsetVersion=9.4&amp;locale=en</A></P> Sun, 13 Sep 2020 04:46:01 GMT WarrenKuhfeld 2020-09-13T04:46:01Z why when i have decimals in the matrix I don't get the exact inverse? in SAS IML https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/why-when-i-have-decimals-in-the-matrix-I-don-t-get-the-exact/m-p/683222#M5285 <P>I found the inverse and the transpose of a matrix. Now i want to check whether the matrix is orthogonal. The idea i used is to subtract the transpose and the inverse to get 0, but i found that the deference with some elements is 2.22 E-16. Although it is very small but i need to know why i don't get the exact 0.</P><P>I need help.</P> Fri, 11 Sep 2020 11:43:51 GMT https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/why-when-i-have-decimals-in-the-matrix-I-don-t-get-the-exact/m-p/683222#M5285 Amink 2020-09-11T11:43:51Z Re: why when i have decimals in the matrix I don't get the exact inverse? in SAS IML https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/why-when-i-have-decimals-in-the-matrix-I-don-t-get-the-exact/m-p/683225#M5286 <P>This is called <A href="https://en.wikipedia.org/wiki/Machine_epsilon" target="_self">machine precision</A>. Some floating point (or decimal) numbers can only be represented to within + or minus a small value epsilon, they cannot be represented exactly by a binary computer; and so this carries through the mathematical operations. Your result is essentially zero in the world of computers.</P> Fri, 11 Sep 2020 12:15:52 GMT https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/why-when-i-have-decimals-in-the-matrix-I-don-t-get-the-exact/m-p/683225#M5286 PaigeMiller 2020-09-11T12:15:52Z Re: why when i have decimals in the matrix I don't get the exact inverse? in SAS IML https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/why-when-i-have-decimals-in-the-matrix-I-don-t-get-the-exact/m-p/683488#M5287 <P><a href="https://communities.sas.com/t5/user/viewprofilepage/user-id/10892">@PaigeMiller</a>&nbsp;is correct. The thing I would add is look at the proc compare documentation for various ways to compare computed numbers. Expecting differences to be zero for nontrivial (or ever some fairly trivial) computations is unrealistic. Also check out:&nbsp;<A href="https://documentation.sas.com/?docsetId=lrcon&amp;docsetTarget=p0ji1unv6thm0dn1gp4t01a1u0g6.htm&amp;docsetVersion=9.4&amp;locale=en" target="_blank">https://documentation.sas.com/?docsetId=lrcon&amp;docsetTarget=p0ji1unv6thm0dn1gp4t01a1u0g6.htm&amp;docsetVersion=9.4&amp;locale=en</A></P> Sun, 13 Sep 2020 04:46:01 GMT https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/why-when-i-have-decimals-in-the-matrix-I-don-t-get-the-exact/m-p/683488#M5287 WarrenKuhfeld 2020-09-13T04:46:01Z