LEADER 04348nam 2200541 450 001 9910786794903321 005 20230414230133.0 010 $a1-4832-7498-5 035 $a(CKB)3710000000201965 035 $a(EBL)1888531 035 $a(SSID)ssj0001455538 035 $a(PQKBManifestationID)11883676 035 $a(PQKBTitleCode)TC0001455538 035 $a(PQKBWorkID)11407622 035 $a(PQKB)11493752 035 $a(MiAaPQ)EBC1888531 035 $a(EXLCZ)993710000000201965 100 $a20150109h19591959 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMatrix calculus /$fE. Bodewig 205 $aThird edition. 210 1$aAmsterdam :$cNorth-Holland Publishing Company,$d1959. 210 4$dİ1959 215 $a1 online resource (465 pages) $cillustrations 300 $aIncludes index. 311 0 $a1-322-47855-4 311 0 $a1-4832-3214-X 327 $aFront Cover; Dedication; Matrix Calculus; CopyrightPage; Table of Contents; 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|,?i; 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 327 $aA. 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 327 $aCHAPTER 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 327 $aCHAPTER 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 327 $aCHAPTER 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 {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 330 $aMatrix Calculus 606 $aMatrices 615 0$aMatrices. 676 $a512.896 700 $aBodewig$b Ewald$01522608 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786794903321 996 $aMatrix calculus$93762383 997 $aUNINA