Front Cover -- Matrix Calculus -- Copyright Page -- Table of Contents -- Dedication -- PREFACE -- 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. AlTKENS TRIPLE PRODUCT -- 2.9. ILL-CONDITIONED EQUATIONS -- 2.10. NEIGHBOUR 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 - U P CONVERGENCE BY CHANGING MATRIX -- 10.1. CESARl'S METHOD -- 10.2. VAN DER CORPUT'S DEVICE -- 10.3. THE METHOD OF ELIMINATION -- 10.4. JACOBl'S METHOD -- CHAPTER 11. THE ITERATED DIRECT METHODS -- 11.1. CONVERGENCE OF THE METHOD -- CHAPTER 12. METHODS FOR ELECTRONIC COMPUTERS -- 12.1. KACMARZ'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 IIII: NVERSION 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. EIGEN PROBLEMS -- CHAPTER 1. INTRODUCTORY -- A. ITERATION METHODS -- CHAPTER 2. THE ITERATED VECTORS 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 NEIGHBOUR 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. KRYLOW-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.