6. Introduction to Linear AlgebraΒΆ

As was discussed in our Introduction to Data Analysis and Tools, linear algebra is perhaps the branch of mathematics that is most useful to engineers. However, it is often overshadowed by King Calculus. Our coverage here of linear algebra in no way covers the depth of material found in a math course on linear algebra, such as Dr. Strang’s free online course [STRANG99]. Our focus is distinctly applied to the computation of engineering problems.

Dr. Strang has provided a introduction to linear algebra: LinAlg_nutshell.pdf. If you’d like more information on vectors, matrices, matrix multiplication, and transforming vectors, look at the following Khan Academy videos:

There are at least four very important applications of linear algebra to engineering problems:

  1. Problems related to spacial vectors and geometry
  2. Solutions to systems of linear equations
  3. Vector projections with application to least squares regression and other optimization problems
  4. Solutions to systems of differential equations and eigenvalue problems

We will give adequate coverage to the first three applications and briefly review the salient points of the final application.

Note

On pages of the study guide, where scalar variables are mixed with variables representing vectors and matrices, I will attempt to distinguish them by displaying vectors and matrices in a bold font while keeping scalars in a normal font. On pages where all of the variables are vectors and matrices, I may not be as disciplined to display the vector/matrix variables in bold. It should be obvious from the context on those pages that all variables are vectors and matrices.

In general, vector variables will be lower-case letters and matrices variables will be upper-case letters.

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