A. C. Aitken and the consolidation of matrix theory

Linear Algebra and Its Applications

Volumn 264, Issue 1-3, 1997, Pages 3-12

  Farebrother, Richard William ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039976469     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0024-3795(96)00398-9     Document Type: Article

References (60)

1. Aitken, A. C. 1935. On least squares and linear combination of observations, Proc, Roy. Soc. Edinburgh Part A 55:42-47.
2. Aitken, A. C. 1939a. Determinants and Matrices, Oliver and Boyd, Edinburgh; reprinted by Greenwood Press, London, 1983.
3. Aitken, A. C. 1939b. Statistical Mathematics, Oliver and Boyd, Edinburgh.
4. Aitken, A. C. 1995. To Catch the Spirit, Univ. of Otago Press, Dunedin.
5. Anderson, T. W. 1958. An Introduction to Multivariate Statistical Analysis, Wiley, New York.
6. Anderson, T. W., 1995. Personal communication.
7. Armitage, P. 1996. Personal communication.
8. Bôcher, 1907. Introduction to Higher Algebra, Macmillan, New York.
9. A. L. Cauchy, 1829. Sur 1' équation à l' aide de laquelle on détermine les inégalités séculaires des mouvements des planètes, Exercises Math. 4:140-160; reprinted in Oeuvres (Ser. 2) Vol. 9, Gauthier-Villar, Paris, 1891, pp. 174-195.
10. A. L. Cauchy, 1829. Sur 1' équation à l' aide de laquelle on détermine les inégalités séculaires des mouvements des planètes, Exercises Math. 4:140-160; reprinted in Oeuvres (Ser. 2) Vol. 9, Gauthier-Villar, Paris, 1891, pp. 174-195.
11. Cayley, A. 1858. Memoir on the theroy of matrices, Philos. Trans. Roy. Soc. London 148:17-37 (1858).
12. Courant, R. and Hubert, D. 1924, 1938. Methods of Mathematical Physics, 2 vols., Julius Springer, Berlin; English transl. Interscience, New York, 1953.
13. Cullis, C. E. 1913-1925. Matrices and Determinoids, 3 vols., Cambridge U. P. Cambridge.
14. Dorfman, R., Samuelson, P. A., and Solow, R. M. 1958. Linear Programming and Economic Analysis, McGraw-Hill, New York.
15. Eisenstein, G. 1844. Algemeine Untersuchungen über die Formen dritten Grades mit drei Variabeln, welche der Kreistheilung ihre Entstehung verdanken, J. Reine Angew. Math. 28:289-374.
16. Ferrar, W. L. 1941. Algebra: A Text-book of Determinants, Matrices and Algebraic Forms, Oxford U. P., Oxford, 1941.
17. Fisher, R. A. 1936. The use of multiple measurements in taxonomic problems, Ann. Eugen. 7:179-188.
18. Fisher, R. A. 1938. The statistical utilisation of multiple measurements, Ann. Eugen. 8:376-386.
19. Frazer, R. A., Duncan, W. J., and Collar, A. R. 1938. Elementary Matrices and Some Applications to Dynamics and Differential Equations, MacMillan, London; reprinted by AMS Press, New York, 1982.
20. Frobenius, G. 1877. Ueber das Pfaffsche Problem, J. Reine Angew. Math. 82:230-315.
21. Gauss, C. F. 1801. Disquisitiones Arithmeticae, Gerhardt Fleischer; reprinted in his Werke, Vol. 1, Univ. of Göttingen, Göttingen, 1870.
22. Gauss, C. F. 1801. Disquisitiones Arithmeticae, Gerhardt Fleischer; reprinted in his Werke, Vol. 1, Univ. of Göttingen, Göttingen, 1870.
23. Grattan-Guinness, I. 1994. "A new type of question". On the prehistory of linear an nonlinear programming, Hist. Modern Math. 3:43-89.
24. Grattan-Guinness, I. and Ledermann, W. 1994. Matrix theory, in (I. Grattan-Guiness, Ed.) Companion Encyclopedia to the History and Philosophy of the Mathematical Sciences Routledge, London, pp. 775-786.
25. Halmos, P. R. 1942. Finite-Dimensional Vector Spaces, Princeton U. P., Princeton, N.J.
26. Hawkins, T. W. 1975. The theory of matrices in the 19th century, in Proceedings of the International Congress of Mathematics, Vancouver, Canada, Vol. 2, pp. 561-570.
27. Hermite, C. 1854. Sur la Théorie des formes quadratiques ternaires indéfines, J. Reine Angew. Math. 47; reprinted in his Oeuvres vol. 1, Gauthier-Villars, Paris, 1905, pp. 193-199.
28. Hermite, C. 1854. Sur la Théorie des formes quadratiques ternaires indéfines, J. Reine Angew. Math. 47; reprinted in his Oeuvres vol. 1, Gauthier-Villars, Paris, 1905, pp. 193-199.
29. Jacobi, C. G. J. 1827. Über die Pfaffsche Methode, eine gewöhnliche lineare Differentialgleichung zwischen 2n Variabeln durch ein System von n Gleichungen zu integrieren, J. Angew. Math. 2:347-357; reprinted in his Werke, Vo. 4, Reimer, Berlin, 1886, pp. 17-29.
30. Jacobi, C. G. J. 1827. Über die Pfaffsche Methode, eine gewöhnliche lineare Differentialgleichung zwischen 2n Variabeln durch ein System von n Gleichungen zu integrieren, J. Angew. Math. 2:347-357; reprinted in his Werke, Vo. 4, Reimer, Berlin, 1886, pp. 17-29.
31. Johnston, J. 1963. Econometric Methods, McGraw-Hill, New York.
32. Kendall, M. G. 1957. A Course in Multivariate Analysis, Griffin, London.
33. Koopmans, T. C. 1950. Statistical Inference in Dynamic Economic Models, Wiley, New York.
34. Lagrange, J. L. 1775. Nouvelle solution du problème du rotation d'un corps de figure quelconque qui n'est animé par acune force accélératrice, Nouv. Mem. Acad. Berlin; reprinted in his Oeuvres, Vol. 3, Gauthier-Villars, Paris, 1869, pp. 577-616.
35. Lagrange, J. L. 1775. Nouvelle solution du problème du rotation d'un corps de figure quelconque qui n'est animé par acune force accélératrice, Nouv. Mem. Acad. Berlin; reprinted in his Oeuvres, Vol. 3, Gauthier-Villars, Paris, 1869, pp. 577-616.
36. Ledermann, W. W. 1968. A. C. Aitken's work in pure mathematics, Proc. Edinburgh Math. Soc. Ser. 2 16;162-165.
37. Lindley, D. V. 1996. Personal communication.
38. MacDuffee, C. C. 1933. The Theory of Matrices, Julius Springer, Berlin; reprinted by Chelsea, New York.
39. Mirsky, L. A. 1955. An Introduction to Linear Algebra, Oxford U. P., Oxford.
40. Olkin, I. 1955. A. C. Aitken on compounds, presented at the Fourth International Workshop on Matrix Methods for Statistics, Montreal, Canada.
41. Plackett, R. L. 1960. Principles of Regression Analysis, Oxford U. P., Oxford.
42. Plackett, R. L. 1996. Personal communications.
43. Rao, C. R. 1965. Linear Statistical Inference and Its Applications, Wiley, New York.
44. Schreier, O., and Sperner, E. 1951. Introduction to Modern Algebra and Matrix Theory, Chelsea, New York.
45. Seber, G. A. F. 1966. The Linear Hypothesis: A General Theory, Griffin, London.
46. Sturm, C. 1829. Extrait d'un mémoire sur l'intégration d' un système d' équations différentielles linéaires, Bull. Sci. Math. 12:313-322.
47. Sylvester, J. J. 1850. Additions to the articles, "On a new class of theorems," and "On Pascal's theorem," Philos. Mag. Ser. 3 37:363-379; reprinted in his Mathematical Papers, Vol. 1, Cambridge U. P., Cambridge, 1904, pp. 145-151.
48. Sylvester, J. J. 1850. Additions to the articles, "On a new class of theorems," and "On Pascal's theorem," Philos. Mag. Ser. 3 37:363-379; reprinted in his Mathematical Papers, Vol. 1, Cambridge U. P., Cambridge, 1904, pp. 145-151.
49. Sylvester, J. J. 1851. On the relation between the minor determinants of linearly equivalent quadratic forms, Philos. Mag. Ser. 4 1:295-305; reprinted in his Mathematical Papers, Vol. 1, Cambridge U. P., Cambridge, 1904, pp. 241-249.
50. Sylvester, J. J. 1851. On the relation between the minor determinants of linearly equivalent quadratic forms, Philos. Mag. Ser. 4 1:295-305; reprinted in his Mathematical Papers, Vol. 1, Cambridge U. P., Cambridge, 1904, pp. 241-249.
51. Sylvester, J. J. 1883. On the equation to the secular inequalities in the planetary theory, Phil. Mag. Ser. 5 16:267-269.
52. Tee, G. 1980. Two New Zealand Mathematicians, in First Australian Conference on the History of Mathematics, Monash U., Clayton, Australia, pp. 182-199.
53. Turnbull, H. W., and Aitken, A. C. 1932. An Introduction to the Theory of Canonical Matrices, Blackie, London; reprinted by Dover, New York, 1961.
54. van der Waerden, B. L. 1931. Moderne Algebra J. Springer, Berlin.
55. Watson, G. S. 1995, 1996. Personal communications.
56. Wedderburn, J. H. M. 1934. Lectures on Matrices, AMS Press, New York; reprinted by AMS Press, Providence, 1960, and Dover, New York, 1964.
57. Weierstrass., K. 1868. Aur Theorie der bilinearen und quadratischen Formen, Monatsber. Berlin. Akad. Wiss. reprinted in his Mathematische Werke, Vol. 2, Mayer und Muller, Berlin, 1895 pp. 19-44.
58. Whittaker, E. T., and Robinson, G. 1924. The Calculus of Observations, Blackie, London; 4th ed. (1944) reprinted by Dover, New York, 1967.
59. Whittaker, J. M. 1968. Alexander Craig Aitken, 1895-1967, Biograph. Mem. Fellows Soc. London 14:1-8.
60. Wilkinson, J. H. 1965. The Algebraic Ekgenvalue Problem, Oxford U. P., Oxford, 1965.