29 Section Summary

It is time to conclude this chapter on linear algebra. An interesting aspect is we are, at least in a relative sense, much more familiar with the topics dealt in linear algebra. As we discussed in the introduction, through the training in elementary algebra, we have learnt how to solve linear equations of some basic forms. The major difference here is the systematic approach, as a series or collection of linear equations is referred to as a system of linear equations or simply a linear system.

Regrettably, due to the limitation on the length of the summary, we could not cover many topics of importance. In case of matrix decomposition, diagonalization is just one of matrix decomposition techniques, and there are many other useful and important methods – LU decomposition into lower- and upper-triangle matrices, Cholesky decomposition, and rank factorization are some examples.

It is noteworthy linear algebra has many practical applications. One popular and well-known area is operational research with linear programming. There are instances optimal solutions are needed under restrictive conditions, expressed in linear terms, and through the techniques of linear programming or linear optimization we identify such solutions. More will be covered in the following section, mathematical modelling, so stay tuned.