Inequalities | Symmetric functions

Newton's inequalities

In mathematics, the Newton inequalities are named after Isaac Newton. Suppose a1, a2, ..., an are real numbers and let denote the kth elementary symmetric polynomial in a1, a2, ..., an. Then the elementary symmetric means, given by satisfy the inequality If all the numbers ai are non-zero, then equality holds if and only if all the numbers ai are equal. It can be seen that S1 is the arithmetic mean, and Sn is the n-th power of the geometric mean. (Wikipedia).

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From playlist Adventures With Inequalities - GCSE Maths Revision

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From playlist A first course in university mathematics

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From playlist Algebra: Inequalities

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From playlist MATHS

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From playlist Newton above Hodge

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From playlist Lecture Collection | Convex Optimization

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From playlist Lecture Collection | Convex Optimization

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From playlist Linear Inequalities in One Variable Solving Linear Inequalities

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From playlist Lecture Collection | Convex Optimization

Related pages

Elementary symmetric polynomial | Geometric mean | Maclaurin's inequality | If and only if | Mathematics | Inequality (mathematics) | Real number | Isaac Newton | Arithmetic mean