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Mixed-mean inequality for submatrix

In: Mathematica Slovaca, vol. 63, no. 5
Lin Si - Suyun Zhao

Details:

Year, pages: 2013, 1001 - 1006
Keywords:
mixed mean, power mean, matrix, arithmetic-geometric mean inequality
About article:
For an $m× n$ matrix $B=(bij)m× n$ with nonnegative entries $bij$, let $B(k,l)$ denote the set of all $k× l$ submatrices of $B$. For each $A \in B(k,l)$, let $aA$ and $gA$ denote the arithmetic mean and geometric mean of elements of $A$ respectively. It is proved that if $k$ is an integer in $(((m) / (2)), m]$ and $l$ is an integer in $(((n) / (2)), n]$ respectively, then

$$ (\prodA\in B(k,l)aA) ^{\frac{1}{\binom{m}{k}\binom{n}{l}}} ≥\frac{1}{\binom{m}{k}\binom{n}{l}} (∑A\in B(k,l)gA), $$

with equality if and only if $bij$ is a constant for every $i,j$.
How to cite:
ISO 690:
Si, L., Zhao, S. 2013. Mixed-mean inequality for submatrix. In Mathematica Slovaca, vol. 63, no.5, pp. 1001-1006. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0150-1

APA:
Si, L., Zhao, S. (2013). Mixed-mean inequality for submatrix. Mathematica Slovaca, 63(5), 1001-1006. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0150-1
About edition: