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A First Course in Linear Algebra is writtenby two experts from algebra who have morethan 20 years of experience in algebra,linear algebra and number theory. Itprepares students with no background inLinear Algebra. Students, after masteringthe materials in this textbook, can alreadyunderstand any Linear Algebra used in moreadvanced books and research papers inMathematics or in other scientific disciplines.This book provides a solid foundation for thetheory dealing with finite dimensional vectorspaces. It explains in details the relationbetween linear transformations and matrices.One may thus use different viewpoints tomanipulate a matrix instead of a one-sidedapproach. Although most of the examplesare for real and complex matrices, a vectorspace over a general field is briefly discussed.Several optional sections are devoted toapplications to demonstrate the power ofLinear Algebra.