Book:A.C. Aitken/Determinants and Matrices/Eighth Edition
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A.C. Aitken: Determinants and Matrices (8th Edition)
Published $\text {1954}$, Oliver & Boyd
Subject Matter
Contents
- Chapter $\text I$: Definitions and Fundamental Operations of Matrices
- 1. Introductory
- 2. Linear Equations and Transformations
- 3. The Notation of Matrices
- 4. Matrices, Row and Column Vectors, Scalars
- 5. The Operations of Matrix Algebra
- 6. Matrix Pre- and Postmultiplication
- 7. Product of Three or More Matrices
- 8. Transposition of Rows and Columns
- 9. Transpose of a Product: Reversal Rule
- 10. Algebraic Expressions in Matrix Notation
- 11. Partitioned Matrices and Multiplication
- Chapter $\text {II}$: Definition and Properties of Determinants
- 12. The Solution of Simultaneous Equations
- 13. Salient Properties of Eliminants
- 14. Inversions and Class of Permutations
- 15. Definition and Notation of Determinant
- 16. Identity of Class of Conjugate Permutations
- 17. Elementary Properties of Determinants
- 18. Primeness of a Determinant
- 19. Various Expansions of a Determinant
- 20. Pivotal Evaluation of Determinants
- Chapter $\text {III}$: Adjugate and Reciprocal Matrix: Solution of Simultaneous Equations: Rank and Linear Dependence
- 21. The Adjugate Matrix of a Square Matrix
- 22. Solution of Equations in Nonsingular Case
- 23. Reversal Rule for Reciprocal of Product
- 24. Orthogonal and Unitary Matrices
- 25. Solution of Homogeneous Equations
- 26. Rank and Nullity of Matrix
- 27. Linear Dependence
- 28. Conditions for Solution of Homogeneous Equations
- 29. Reduction of Matrix to Equivalent Form
- 30. Solution of Non-Honogeneous Equations
- Chapter $\text {IV}$: Cauchy and Laplace Expansions: Multiplication Theorems
- 31. Expansion by Elements of Row and Column
- 32. Complementary Minors and Cofactors
- 33. Laplacian Expansion of a Determinant
- 34. Multiplication of Determinants
- 35. Extended Laplace and Cauchy Expansions
- 36. Determinant of Product of Rectangular Matrices
- 37. Expansion by Diagonal Elements: Normal Form
- Chapter $\text V$: Compound Matrices and Determinants: Dual Theorems
- 38. Compound and Adjugate Compound Matrices
- 39. Binet-Cauchy Theorem on Product of Compounds
- 40. Reciprocal of Nonsingular Compound Matrix
- 41. Rank Expressed by Compound Matrices
- 42. Jacobi's Theorem on Minors of Adjugate
- 43. Franke's Theorem on Minors of Compound
- 44. Hybrid Compounds of Bazin and Reiss
- 45. Complementary and Extensional Identities
- 46. Schweinsian Expansions of Determinant Quotients
- Chapter $\text {VI}$: Special Determinants: Alternant, Persymmetric, Bigradient, Centrosymmetric, Jacobian, Hessian, Wronskian
- 47. Alternant Matrices and Determinants
- 48. Elementary and Complete Symmetric Functions
- 49. Bialternant Symmetric Functions of Jacobi
- 50. Confluent or Differentiated Alternants
- 51. Persymmetric, Circulant and Centrosymmetric
- 52. Dialytic Elimination: Bigradients
- 53. Continuant Matrices and Continuants
- 54. Jacobians, Hessians and Wronskians
- Additional Examples
- Index
Further Editions
- 1939: A.C. Aitken: Determinants and Matrices
- 1942: A.C. Aitken: Determinants and Matrices (2nd ed.)
- 1944: A.C. Aitken: Determinants and Matrices (3rd ed.)
- 1946: A.C. Aitken: Determinants and Matrices (4th ed.)
- 1948: A.C. Aitken: Determinants and Matrices (5th ed.)
- 1949: A.C. Aitken: Determinants and Matrices (6th ed.)
- 1951: A.C. Aitken: Determinants and Matrices (7th ed.)
Source work progress
- 1954: A.C. Aitken: Determinants and Matrices (8th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions and Fundamental Operations of Matrices: $5$. The Operations of Matrix Algebra