Matrix Decomposition

Question

I have a square n*n matrix S that has to be decomposed into a product of two matrices - A1 and A2, where A2 is transposed matrix to A1 (A2=A1^T) , so A1 * A2 = S. Are there any algorithms to do such operation effectively? C#/C++ solution would be nice.

Answer 1

As Andrei suggested, it seems you are trying to do Cholesky Decomposition.

There is provided C++ code in polish wiki site for it .

There is also separate subsection in "Numerical recipes in C" (2.9 Cholesky decomposition, can be found here: http://www.nrbook.com/a/bookcpdf/c2-9.pdf )

Answer 2

在这种情况下，您可能需要http://en.wikipedia.org/wiki/Cholesky_decomposition

Answer 3

I'm not quite sure what you want to do but

here is the GSL lib that might help

14 Linear Algebra