Libraries.

The linear algebra library that is used in the algorithms is called
`newmat`, which is a public domain library. The current version is found
as a file `newmat09.zip` or `newmat09.tar.gz` on major ftp
archives. Search using `archie`. The usage in the algorithms should be
pretty clear from the context, and other linear algebra `C++` libraries will have
similar notation, but here are some examples:

Defining the variables:

`Matrix A;`

`ColumnVector b;`

Calculations:

Take inverse, : `Matrix Ainv = A.i();`

Matrix multiply,
: `Matrix C = A * b.t();`

Solve system, : `Matrix x = A.i()*b;`

For linear algebra, it is possible to take advantage of particular forms of
matrices, such as banded matrices, diagonal matrices etc. `C++` is
particularly useful here, a good linear algebra library will choose efficient
algorithms depending on the form of the matrices, without the need for
particular choice of subroutines by the programmer, the choice of algorithm is
purely made from context. For an example of this, look at the algorithm for
option pricing using implicit finite differences.