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Matrix Calculus
- 3rd Edition - May 12, 2014
- Author: E. Bodewig
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 5 5 3 9 - 2
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 4 9 8 - 0
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… Read more
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Request a sales quoteMatrix 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.
Part I. Matrix Calculus 1. Vectors 1.1. Equation of a Plane 2. Matrices 3. Further Applications 4. Measures of the Magnitude of a Matrix 5. Forms 6. Eigenvalues 6.1. Modal Matrix, Spectral Matrix 6.2. Characteristic Equation 6.3. Relations 6.4. Eigenrows 6.5. Extremum Properties 6.6. Bounds for Eigenvalues 6.7. Bounds for the Determinant 6.8. Elementary DivisorsPart II. Linear Equations A. Direct Solutions 1. Exact Solutions .2 Approximate Solutions B. Iteration Methods 3.1. Introduction 3.2. Preliminary View 3.3. Development of Iteration Methods 4. Iteration I, II 5. Characteristic Equation of Iteration Processes 6. Type of Convergence of Iteration Methods 7. Convergence Theorems 8. General Iteration 9. Methods for Automatic Machines 10. Speeding-up Convergence by Changing Matrix 11. The Iterated Direct Methods 12. Methods for Electronic Computers 13. Various QuestionsPart III. Inversion of Matrices A. Direct Methods 1. Condensation 2. Frobenius's Relation 3. Completing 4. TheAdjugate B. Iteration Method C. Geodetic MatricesPart IV. Eigenproblems 1. Introductory A. Iteration Methods 2. The Iterated Vectors (Power Method) 3. Orthogonal Transformations 4. Method of Solving Linear Equations 5. The Gradient Method 6. The Use of Polynomials 7. Powers of the Matrix 8. Deflation 9. Rutishauser's LR-Algorithm B. Direct Methods 10. Determination of Eigenvectors 11. Pure Methods 12. Progressive Algorithms 13. The Eigenproblem (A + λB)x = 0 14. Special MatricesExercisesLiteratureIndex
- No. of pages: 466
- Language: English
- Edition: 3
- Published: May 12, 2014
- Imprint: North Holland
- Paperback ISBN: 9781483255392
- eBook ISBN: 9781483274980
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