Energy Fundamentals of Radio

Chapter 9A Note on Linear Algebra

With this chapter, we continue with the familiar challenge of dealing with a big, rich topic in a short span. Our approach remains constant, which is that we start with applications that we need to understand and then work backward, prioritizing the topics that are needed. For radio, the most important applications are the DFT (or FFT), least squares, and multi-antenna systems. We had a preview of our analytical needs with the discussion of the DFT in Chapter 2. Singular value decomposition is central to the multi-antenna techniques of Chapter 10, and it will turn out that least squares techniques figure prominently in understanding digital predistortion in Chapter 11.

9.1 What Problem Are We Solving with a Matrix?

Most engineers run across matrices at some point in their professional trajectory. If you are a control theorist or practitioner, you live with this stuff and can recite more matrix fun facts in a minute than most other engineers ever learn. And if you subjected yourself to a formal linear algebra course in college, you may have vague memories of how matrices helped to solve systems of equations; the importance of something called the “determinant,” and how it had something to do with inversion; special vectors called eigenvectors; etc.

After many years of study and application in various contexts, the author suggests that the broadest application, and the most useful foundational understanding, of matrices, is to see them as a ...