I have a matrix A with real values that I wish to decompose into a proper orthogonal matrix R and a symmetric matrix U.(adsbygoogle = window.adsbygoogle || []).push({});

Now the matrix A is obtained from a process such that this decomposition isusuallypossible, and U turns out to be also positive definite.

The problem arises when I get a matrix that is "close" to an identity matrix, i.e, its components differ from the identity matrix by random values on the order 1e-3.

Here, sometimes I get non-numeric (NaN) values when I attempt to do the decomposition. I can disregard these 'bad' matrices altogether, but I do not know how to check for such a 'bad' matrix.

Is there a condition on A such that A=RU is possible for real-valued matrices? I can guess this question reduces to the existence of matrix square root for A^{T}A, but not sure of how to proceed further...

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Condition for existence of polar decomposition for a real matrix?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**