Matrix Calculus 3rd Edition by E Bodewig – Ebook PDF Instant Download/Delivery: 1483274985, 9781483274980
Full download Matrix Calculus 3rd edition after payment
Product details:
ISBN 10: 1483274985
ISBN 13: 9781483274980
Author: E Bodewig
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.
Matrix Calculus 3rd Table of contents:
PART I: MATRIX CALCULUS
CHAPTER I. VECTORS
1.1. Equation of a Plane
CHAPTER II. MATRICES
CHAPTER 3. FURTHER APPLICATIONS
CHAPTER 4. MEASURES OF THE MAGNITUDE OF A MATRIX
CHAPTER 5. FORMS
CHAPTER 6. EIGENVALUES
6.1. Modal-Matrix, Spectral-Matrix
6.2. The Characteristic Equation
6.3. Relations between Sp, N, |A|, λi
6.4. Eigenrows
6.5. Extremum Properties of the Eigenvalues
6.6. Bounds for the Eigenvalues
6.7. Bounds for the Determinant
6.8. Elementary Divisors
PART II: LINEAR EQUATIONS
A. DIRECT METHODS
CHAPTER 1. EXACT SOLUTIONS
1.1. Elimination I
1.2. Elimination II
CHAPTER 2. APPROXIMATE SOLUTIONS
2.1. Condensation I. Triangularisation
2.2. Condensation II. Diagonalization
2.3. The Decomposition of the Matrix into Two Triangular Matrices
2.4. Choice of Another Pivotal Element
2.5. The Gauss-Doolittle Process
2.6. A Method for Punched Cards
2.7. The Generalized Condensations I and II
2.8. Aitken’s Triple Product
2.9. Ill-Conditioned Equations
2.10. Neighbor Systems
2.11. Errors and Exactness of the Solution
2.12. Complex Systems
B. ITERATIONS METHODS
CHAPTER 3.
3.1. Introduction
3.2. Preliminary View
3.3. Development of the Iteration Methods
CHAPTER 4. ITERATION I
CHAPTER 5. THE CHARACTERISTIC EQUATION OF THE ITERATION PROCESSES
CHAPTER 6. TYPE OF CONVERGENCE OF THE ITERATION METHODS
CHAPTER 7. CONVERGENCE THEOREMS
7.1. Schmidt-Mises-Geiringer
7.3. Iteration II
7.4. Iteration I
7.5. Geiringer’s Theorem
7.6. Theorem of Stein and Rosenberg
7.7. Another Theorem of Stein-Rosenberg
7.8. Aitken’s Neo-Seidelian Iteration
CHAPTER 8. THE GENERAL ITERATION
CHAPTER 9. METHODS FOR AUTOMATIC MACHINES
CHAPTER 10. SPEEDING-UP CONVERGENCE BY CHANGING MATRIX
10.1. Cesari’s Method
10.2. Van Der Corput’s Device
10.3. The Method of Elimination
10.4. Jacob’s Method
CHAPTER 11. THE ITERATED DIRECT METHODS
11.1. Convergence of the Method
CHAPTER 12. METHODS FOR ELECTRONIC COMPUTERS
12.1. Kaczmarz’s Procedure
12.2. Cimmino’s Procedure
12.3. Linear Equations as Minimum Condition
12.4. Linear Equations as Eigenproblems
CHAPTER 13. VARIOUS QUESTIONS
13.1. Normalization
13.2. Scaling
13.3. Another Scaling
13.4. A Third Scaling
PART III: INVERSION OF MATRICES
A. DIRECT METHODS
CHAPTER 1. CONDENSATION
1.1. The Inverse of a Triangular Matrix
CHAPTER 2. FROBENIUS-SCHUR’S RELATION
CHAPTER 3. COMPLETING
CHAPTER 4. THE ADJUGATE
4.1. The Method of Determinants
B. ITERATION METHOD
C. GEODETIC MATRICES
PART IV: EIGENPROBLEMS
CHAPTER 1. INTRODUCTORY
A. ITERATION METHODS
CHAPTER 2. THE ITERATED VECTORS (Power Method)
2.1. The Dominant Eigenvalue is Real
2.2. The Dominant Eigenvalue is Complex
2.3. Other Cases
2.4. Criticism of the Power Method
2.5. Higher Eigenvalues
2.6. Higher Eigenvalues According to Aitken
2.7. The Least Eigenvalues
2.8. The Use of Frobenius’s Theorem
2.9. Wilkinson’s Method
2.10. Multiple Eigenvalues
CHAPTER 3. ORTHOGONAL TRANSFORMATIONS
3.1. Jacobi’s Method
3.2. Magnier’s and Jahn’s Modification
3.3. Givens’s Method
CHAPTER 4. THE METHOD OF SOLVING LINEAR EQUATIONS
4.1. The Iteration with A-1
CHAPTER 5. THE GRADIENT METHOD
CHAPTER 6. THE USE OF POLYNOMIALS
CHAPTER 7. POWERS OF THE MATRIX
CHAPTER 8. DEFLATION
8.1. Hotelling’s Deflation
8.2. Wielandt’s Deflation
8.3. A Third Deflation
8.4. A Fourth Deflation
8.5. Vector-Deflation. Scalar Deflation
8.6. Wedderburn’s Theorem
8.7. Matrix Deflation in the Case of Higher Elementary Divisors
CHAPTER 9. RUTISHAUSER’S LR-ALGORITHM
B. DIRECT METHODS
CHAPTER 10. DETERMINATION OF THE EIGENVECTORS
10.1. Eigenvalues for Neighbor Equations
10.2. Influence of Matrix Errors
10.3. Changes of the Roots of D(λ)
10.4. The Number of Operations
CHAPTER 11. PURE METHODS
11.1. Leverrier’s Method
11.2. Krylov-Duncan’s Method
11.3. Samuelson’s Method
11.4. Other Methods
CHAPTER 12. PROGRESSIVE ALGORITHMS
12.1. A Method
12.2. Lanczos’s pq-Algorithm
12.3. Hessenberg’s Method
CHAPTER 13. THE EIGENPROBLEM (A + λB)x = 0
CHAPTER 14. SPECIAL MATRICES
EXERCISES
LITERATURE
INDEX
People also search for Matrix Calculus 3rd:
matrix editions vector calculus
matrix calculus book
matrix calculus e. bodewig pdf
matrix editions
bodewig matrix calculus
Tags:
E Bodewig,Matrix Calculus