An Inequality for Elementary Symmetric Functions
1972 ◽
Vol 15
(1)
◽
pp. 133-135
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Keyword(s):
Let Er denote the rth elementary symmetric function on α1 α2,…,αm which is defined by1E0 = 1 and Er=0(r>m).We define the rth symmetric mean by2where denote the binomial coefficient. If α1 α2,…,αm are positive reals thenwe have two well-known inequalities3and4In this paper we consider a generalization of these inequalities. The inequality (4) is known as Newton's inequality which contains the arithmetic and geometric mean inequality.
Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
1959 ◽
Vol 11
◽
pp. 383-396
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1969 ◽
Vol 12
(5)
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pp. 615-623
◽
2001 ◽
Vol 14
(3)
◽
pp. 237-248
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1927 ◽
Vol 1
(1)
◽
pp. 55-61
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Keyword(s):
1973 ◽
Vol 74
(1)
◽
pp. 133-139
◽
1978 ◽
Vol 84
(1)
◽
pp. 1-3
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Keyword(s):
1962 ◽
Vol 58
(2)
◽
pp. 420-421
◽
1967 ◽
Vol 19
◽
pp. 281-290
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1888 ◽
Vol 7
◽
pp. 41-42