The applications are interesting and varied, but limited in length and depth. Many of these topics are not included in most introductory courses, but current introductory texts often include them in optional chapters to provide instructors with topics for projects and to provide students with additional material to read on their own. Although complex vector spaces are used in the sections on diagonalization and Jordan form, there is no discussion of hermitian, skew-hermitian, unitary, or normal matrices. Operation counts and iterative methods (other than the method of powers for sparse matrices) are not discussed. Numerical linear algebra is mentioned only in the context of Gaussian elimination and the method of powers, which appear as Topics at the ends of Chapters One and Five. Neither are pseudoinverses or the singular value decomposition, which means that diagonalization of non-square matrices is never mentioned. Positive definite and positive semidefinite matrices are not covered. The spectral theorem for symmetric matrices is not mentioned. Least squares is an add-on end-of-chapter Topic, and only lines of best fit are discussed. Orthogonality is viewed as an optional, not a central, topic. Matrix factorizations (LU, QR, etc.) are not covered. He emphasizes concepts and theory much more than calculation, and linear transformations much more than matrices. The author does not focus on the four fundamental subspaces, a point of view popularized by Gilbert Strang in his books Linear Algebra and Its Applications and Introduction to Linear Algebra. Optional sections in Chapter Five give a more comprehensive treatment of Jordan canonical form than is found in most introductory texts, many of which omit this topic entirely. (It’s in a section unhelpfully entitled “The Linear Combination Lemma”). Uniqueness of reduced echelon form is proved in detail. This text does a good job of covering the theory in detail, especially in Chapters Two and Five. Reviewed by Daniel Drucker, Professor and Associate Chair, Wayne State University on 12/5/18 Journalism, Media Studies & Communications.
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