Expansion of determinantal equations into polynomial form
Author:
Harold Wayland
Journal:
Quart. Appl. Math. 2 (1945), 277-306
MSC:
Primary 65.0X
DOI:
https://doi.org/10.1090/qam/11799
MathSciNet review:
11799
Full-text PDF Free Access
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Additional Information
James and Coolidge, J. Chem. Phys. 1, 825 (1933).
Duncan and Collar, Phil. Mag. 17, 865 (1934).
Frazer, Duncan and Collar, Elementary matrices, Macmillan, 1938, p. 133.
A. C. Aitken, Proc. Roy. Soc. Edinburgh, 57, 269 (1937).
T. C. Fry, private communication.
M. Masuyama, Proc. Phys. Math. Soc. Japan (3), 21, 100 (1939).
A. N. Krylov, Bull. de l’Acad. Sci. U.R.S.S. (4), 7, 491 (1931).
A. Danielewsky, Trans. Mosc. Math. Soc. 44, 169 (1937).
Frazer, Duncan and Collar, loc. cit., 141—142.
B. Hicks, Thesis, Calif. Inst. of Tech. (1939).
B. Hicks, J. Chem. Phys. 8, 569 (1940).
P. Horst, Ann. Math. Stat. 6, 83 (1935).
- P. A. Samuelson, A method of determining explicitly the coefficients of the characteristic equation, Ann. Math. Statistics 13 (1942), 424–429. MR 7497, DOI https://doi.org/10.1214/aoms/1177731540
O. Reierøl, Ann. Math. Stat. 11, 193 (1941).
F. Chiò, Mémoire sur les fonctions connues sous le nom de résultants ou de déterminants, Turin, 1853. Or, E. T. Whittaker and G. Robinson, The calculus of observations, 2nd. ed., Blackie, 1929, p. 71.
A. C. Aitken, Proc. Roy. Soc. Edinburgh 46, 289 (1926).
A. C. Aitken, Proc. Roy. Soc. Edinburgh 51, 80 (1931).
L. A. Pipes, Jour. Franklin Inst. 225, 437 (1938).
U. J. J. LeVerrier, J. de Math, s.1, 5, 230 (1840).
Dickson, First course in the theory of equations, Wiley, 1922, p. 134.
Muir and Metzler, Theory of determinants, Albany, N. Y., 1930, p. 606.
Frazer, Duncan and Collar, loc. cit., p. 141.
Bôcher, Introduction to higher algebra, Macmillan, 1927, p. 296.
Frazer, Duncan and Collar, loc. cit., p. 90.
Ibid., p. 162.
Whittaker and Robinson, loc. cit., p. 10.
Ibid., p. 28.
A. C. Aitken, Proc. Roy. Soc. Edinburgh 57, 172 (1937).
I. M. H. Etherington, Proc. Edinburgh Math. Soc. (2) 3, 107 (1932).
- F. R. Moulton, On the Solutions of Linear Equations Having Small Determinants, Amer. Math. Monthly 20 (1913), no. 8, 242–249. MR 1517882, DOI https://doi.org/10.2307/2973303
- L. B. Tuckerman, On the mathematically significant figures in the solution of simultaneous linear equations, Ann. Math. Statistics 12 (1941), 307–316. MR 5440, DOI https://doi.org/10.1214/aoms/1177731713
- Paul G. Hoel, The errors involved in evaluating correlation determinants, Ann. Math. Statistics 11 (1940), 58–65. MR 1498, DOI https://doi.org/10.1214/aoms/1177731941
- A. T. Lonseth, Systems of linear equations with coefficients subject to error, Ann. Math. Statistics 13 (1942), 332–337. MR 7121, DOI https://doi.org/10.1214/aoms/1177731572
- Harold Hotelling, Some new methods in matrix calculation, Ann. Math. Statistics 14 (1943), 1–34. MR 7851, DOI https://doi.org/10.1214/aoms/1177731489
James and Coolidge, J. Chem. Phys. 1, 825 (1933).
Duncan and Collar, Phil. Mag. 17, 865 (1934).
Frazer, Duncan and Collar, Elementary matrices, Macmillan, 1938, p. 133.
A. C. Aitken, Proc. Roy. Soc. Edinburgh, 57, 269 (1937).
T. C. Fry, private communication.
M. Masuyama, Proc. Phys. Math. Soc. Japan (3), 21, 100 (1939).
A. N. Krylov, Bull. de l’Acad. Sci. U.R.S.S. (4), 7, 491 (1931).
A. Danielewsky, Trans. Mosc. Math. Soc. 44, 169 (1937).
Frazer, Duncan and Collar, loc. cit., 141—142.
B. Hicks, Thesis, Calif. Inst. of Tech. (1939).
B. Hicks, J. Chem. Phys. 8, 569 (1940).
P. Horst, Ann. Math. Stat. 6, 83 (1935).
P. A. Samuelson, Ann. Math. Stat. 13, 424 (1942).
O. Reierøl, Ann. Math. Stat. 11, 193 (1941).
F. Chiò, Mémoire sur les fonctions connues sous le nom de résultants ou de déterminants, Turin, 1853. Or, E. T. Whittaker and G. Robinson, The calculus of observations, 2nd. ed., Blackie, 1929, p. 71.
A. C. Aitken, Proc. Roy. Soc. Edinburgh 46, 289 (1926).
A. C. Aitken, Proc. Roy. Soc. Edinburgh 51, 80 (1931).
L. A. Pipes, Jour. Franklin Inst. 225, 437 (1938).
U. J. J. LeVerrier, J. de Math, s.1, 5, 230 (1840).
Dickson, First course in the theory of equations, Wiley, 1922, p. 134.
Muir and Metzler, Theory of determinants, Albany, N. Y., 1930, p. 606.
Frazer, Duncan and Collar, loc. cit., p. 141.
Bôcher, Introduction to higher algebra, Macmillan, 1927, p. 296.
Frazer, Duncan and Collar, loc. cit., p. 90.
Ibid., p. 162.
Whittaker and Robinson, loc. cit., p. 10.
Ibid., p. 28.
A. C. Aitken, Proc. Roy. Soc. Edinburgh 57, 172 (1937).
I. M. H. Etherington, Proc. Edinburgh Math. Soc. (2) 3, 107 (1932).
F. R. Moulton, Amer. Math. Monthly 20, 242 (1913).
L. B. Tuckerman, Annals Math. Stat. 12, 307 (1941).
P. G. Hoel, Ann. Math. Stat. 11, 58 (1940).
A. T. Lonseth, Ann. Math. Stat. 13, 332 (1942).
Harold Hotelling, Ann. Math. Stat. 14, 1 (1943).
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Article copyright:
© Copyright 1945
American Mathematical Society
