On Determinants of Symmetric Functions
1927 ◽
Vol 1
(1)
◽
pp. 55-61
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Keyword(s):
The result of dividing the alternant |aαbβcγ…| by the simplest alternant |a0b1c2…| (the difference-product of a, b, c, …) is known to be a symmetric function expressible in two distinct ways, (1) as a determinant having for elements the elementary symmetric functions C, of a, b, c, …, (2) as a determinant having for elements the complete homogeneous symmetric functions Hr. For exampleThe formation of the (historically earlier) H-determinant is evident. The suffixes in the first row are the indices of the alternant; those of the other rows decrease by unit steps. This result is due to Jacobi.
Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
1959 ◽
Vol 11
◽
pp. 383-396
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1972 ◽
Vol 15
(1)
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pp. 133-135
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1943 ◽
Vol 61
(3)
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pp. 300-310
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1969 ◽
Vol 12
(5)
◽
pp. 615-623
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1978 ◽
Vol 84
(1)
◽
pp. 1-3
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Keyword(s):
1962 ◽
Vol 58
(2)
◽
pp. 420-421
◽
2001 ◽
Vol 14
(3)
◽
pp. 237-248
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1888 ◽
Vol 7
◽
pp. 41-42
1934 ◽
Vol 4
(1)
◽
pp. 47-52
Keyword(s):