Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
In Julia, basic linear algebra is built into the standard library. Much of this is achieved using the Basic Linear Algebra System (OpenBLAS) and Linear Algebra PACKage (LAPACK) libraries that ship as shared libraries in binary distros or are built when installing the system from source.
We will begin our study by looking at sets of linear equations and the application of matrix methods to their solutions.
A set of n equations in n unknown quantities will have a unique solution, provided that one of the equations is not a multiple of another. In the latter case, the system is term degenerate since effectively we only have n-1 equations.
Clearly n is a positive number, with n >= 2, since n = 1 is trivial.
The solution of such...