Titlebook: Matrix Algebra; Theory, Computations James E. Gentle Textbook 20071st edition Springer-Verlag New York 2007 Algebra.STATISTICA.algorithm.al

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Numerical Linear Algebraally or with the arrays themselves. Programming languages such as Fortran 77 and C provide the capabilities for working with the individual elements but not directly with the arrays. Fortran 95 and higher-level languages such as Octave or Matlab and R allow direct manipulation with vectors and matrices.

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Vector/Matrix Derivatives and IntegralsThe operations of differentiation and integration of vectors and matrices are logical extensions of the corresponding operations on scalars.

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Evaluation of Eigenvalues and EigenvectorsBefore we discuss methods for computing eigenvalues, we mention an interesting observation. A given .th-degree polynomial .(.) is the characteristic polynomial of some matrix. The companion matrix of equation (3.177) is one such matrix.

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