Recommend please : free math library

Hi,
I am writing a C++ program on network resource assignment and
confliction overcoming. After sort out all kinds of requirement and
constraints, it boils down to some large linear algebra matrix
calculation.

If I work it on a paper by hand, I can work out the solution. But the
problem is I must implement this in C++ programming.

I am wondering how to proceed here? I do not do scientific computing
much, I know there are some Fortran libraries doing this kind of work.

If there such free library for C++? Is there some entry level
tutorial of doing this kind of thing?

Thanks so much!

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