Many students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds. Key Features: o The background needed coincides with typical preparation of students in science and engineering as well as mathematics o The book can be used for both senior undergraduate and first year graduate courses o Each topic in numerical linear algebra is well motivated by the needs of solving problems across science and engineering o Algorithms and their mathematical foundations are developed jointly, each motivating the development of the other, so that students interested in one will expand their knowledge and skill in the other

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