This second volume in a two-volume work describes relevant and modern applications of linear algebra and its fundamental role in physics. It is designed to be read independently as well as in conjunction with Volume 1. It reviews matrix representation and eigenvalue problems as well as change of basis for vectors and mappings, and reviews error correcting codes and proofs. There is discussion of the diagonalization of operators as well as the triangularization of operators with the applications of the triangular form. Attention is paid to inner products and real inner product spaces, with detailed discussion of orthogonal sets, bases, and complements. The author discusses extensively self-adjoint operators (which covers Rayleigh's Principle, positive-definite matrices and Gaussian elimination), least squares approximation, and approximation in inner product spaces. Normal equations are examined while a large section on duality incorporates linear functionals, transformation of covectors, annihilators, and duality and linear equations. Each chapter concludes with a set of proofs and an appendix presents solutions to exercises.
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