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Linear Algebra and Matrices by Shmuel Friedland, Mohsen Aliabadi (Paperback, 2018)

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This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as: constructive discussions about the motivation of fundamental concepts many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks. The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics.