Matrix CalculusElsevier, 2014/05/12 - 466 ページ Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well as the decomposition of the matrix into two triangular matrices, choice of another pivotal element, Gauss-Doolittle process, Aitken's triple product, neighbor systems, errors and exactness of the solution, and complex systems. The publication also elaborates on the characteristic equation of the iteration processes, type of convergence of the iteration methods, speeding-up convergence by changing matrix, and methods for electronic computers. The determination of eigenvectors, pure methods, progressive algorithms, and deflation are also discussed. The manuscript is a helpful reference for researchers interested in matrix calculus. |
多く使われている語句
already applied approximation arbitrary arises become better calculation called characteristic equation coefficients column combination complex component computed convergence corresponding definite deflation derived determinant diagonal diagonal elements direct dominant e-values eigenvalues eigenvectors elementary divisors elements eliminated equal error established exact example factor figures follows former further given gives higher holds improved independent inserted inverse iteration known latter linear machines manner maximum means method multiplications obtained operations orthogonal plane possible principal procedure proof proved quadratic quotient rank relation remain replaced requires resp result roots row and column satisfied sequence side Similarly simple solution solved square starting successively symmetrical symmetrical matrix theorem transformation unknown usual values vanish vector yields zero