8 Further directions in linear algebra - Number Theory Web
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8 Further directions in linear algebra - Number Theory Web
tion to linear Algebra), singular value decomposition (see G. Strang,. Linear
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Further directions in linear algebra 1. Dual space of a vector space; Tensor products of vector spaces; exterior algebra of a vector space. See C.W. Curtis, Linear Algebra, an introductory approach and T.S. Blyth, Module theory. 2. Quadratic forms, positive definite matrices (see L. Mirsky, Introduction to linear Algebra), singular value decomposition (see G. Strang, Linear Algebra). 3. Iterative methods for finding inverses and solving linear systems. See D.R. Hill and C.B. Moler, Experiments in Computational Matrix Algebra. 4. Positive matrices and Markov matrices are important in economics and statistics. For further reading on the structure of Markov matrices and more generally, non–negative matrices, the following books are recommended: [1] N.J. Pullman. Matrix Theory and its Applications, 1976. Marcel Dekker Inc. New York. [2] M. Pearl. Matrix Theory and Finite Mathematics, 1973. McGraw– Hill Book Company, New York. [3] H. Minc. Nonnegative Matrices, 1988. John Wiley and Sons, New York. 5. There are at least two research journals devoted to linear and multilinear algebra in our Physical Sciences Library: Linear and Multilinear Algebra and Linear Algebra and its applications.
