08 closing
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A one-page final chapter, "Further directions in linear algebra," from a linear algebra text in the Matthews folder. It points readers to dual spaces, tensor products and exterior algebra, quadratic forms, positive definite matrices, singular value decomposition, iterative methods for linear systems, and positive and Markov matrices. It cites books by Curtis, Blyth, Mirsky, Strang, Hill and Moler, Pullman, Pearl and Minc, and two linear algebra journals.
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8 Further directions in linear algebra
1. Dual space of a vector space; Tensor products of vector spaces; exte-
rior algebra of a vector space. See C.W. Curtis, Linear Algebra, an
introductory approach and T.S. Blyth, Module theory .
2. Quadratic forms, positive de nite matrices (see L. Mirsky, Introduc-
tion to linear Algebra ), singular value decomposition (see G. Strang,
Linear Algebra ).
3. Iterative methods for nding inverses and solving linear systems. See
D.R. Hill and C.B. Moler, Experiments in Computational Matrix Al-
gebra .
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 multilin-
ear algebra in our Physical Sciences Library: Linear and Multilinear
Algebra andLinear Algebra and its applications .
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