Matrix Fundamentals From Equation Solving to Signal Processing

Matrix Fundamentals introduces tools for working with matrices, their applications, and their significance in the broader context of linear algebra. Assuming no previous exposure to matrices, the first four chapters provide a foundation accessible to students with a basic knowledge of calculus, covering essential matrix methods used in various quantitative fields. The book formulates algorithms and discusses their practical implementation. Later chapters introduce more advanced topics, such as singular value decomposition, along with some modern applications. Emphasizing visualization and experimentation, this text is designed for undergraduate courses for students in STEM, as well as business, economics and social sciences.

Part I.- Introduction: Three Examples.- 1 Systems of Linear Algebraic Equations.- 2 Matrix Algebra.- Part II.- Introduction: The Structure of General Solutions to Linear Algebraic Equations.- 3 Vector Spaces.- 4 Orthogonality in Real Vector Spaces.- Part III.- Introduction: Through the Looking Glass.- 5 Eigenvectors and Eigenvalues of Real Matrices.- 6 Similarity.- 7 Linear Systems of Differential Equations.

Edward Saff's research areas include approximation theory, numerical analysis, and potential theory. He has published more than 295 mathematical research articles, co-authored 9 books, and co-edited 11 volumes. Recognitions of his professional accomplishments include his receipt of Fulbright and Guggenheim Fellowships, an Honorary Doctorate from Taras Schevchenko National University, Kyiv, Ukraine in 2024, his election as a SIAM Fellow (Society for Industrial and Applied Mathematics) in 2023, as a Foreign Member of the Bulgarian Academy of Sciences in 2013, and as a Fellow of the American Mathematical Society in 2013. In addition, he received Vanderbilt University’s Chancellor’s Research Award (2005) and is an ISI Highly Cited Researcher (since 2007).

Dave Snider’s research has focused on differential equations, optimization, random processes, classical mechanics, and matrix analysis. He has consulted in industry in the areas of electrodynamics, heat transfer, orbital instrumentation and control, semiconductor modeling, neuroscience, biomedics, and algorithm design. He has published 10 textbooks (including 3 with Ed Saff) and over 100 research articles, and has held positions at MIT’s Draper Instrumentation Lab, UCLA’s Mathematics Department, and the Mathematics, Physics, and Electrical Engineering Departments at the University of South Florida, where he received the Distinguished Teacher award in 1989.