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Dual Vector Spaces and Multilinear Algebra,ct of two vector spaces and provides an introduction to the subject of what is called multilinear algebra. The last section contains an application of the theory of dual vector spaces to the proof of the elementary divisor theorem, which was stated in Section 25.
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Linear Transformations and Matrices,ansformations. In this chapter we develop the language of linear transformations and the connection between linear transformations and matrices. Deeper results about linear transformations appear later.
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Determinants,t by thinking of the determinant as a function of the row vectors of a matrix of . with respect to some basis. If the matrix of . has real coefficients, the determinant is (up to a sign ± 1) the volume of the parallelopiped whose edges are the rows of the matrix.
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Some Applications of Linear Algebra, The second contains a theorem on the eigenvalues and eigen-vectors of a matrix whose entries are positive real numbers. An application to stochastic matrices and Markov chains is outlined. Finally, we take up an approach, using linear algebra, to a problem in classical algebra, on sums of squares.
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Textbook 1984Latest editiont developed in this way have become part of the language of much of higher mathematics. They also provide a framework for appli cations of linear algebra to many problems in mathematics, the natural sciences, economics, and computer science. This book is the revised fourth edition of a textbook des
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FLING
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Charles W. Curtisrent views of experts from around the world regarding the many aspects of this disorder. It is hoped that we can provide an image of where we stand as we enter the 1990s. If the book can stimulate other physicians and basic scientists to enter this exciting field of research, and if it can provide hope to the978-1-4471-3293-6
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Charles W. Curtisrent views of experts from around the world regarding the many aspects of this disorder. It is hoped that we can provide an image of where we stand as we enter the 1990s. If the book can stimulate other physicians and basic scientists to enter this exciting field of research, and if it can provide hope to the978-1-4471-3293-6