Inequalities for Matrix Powers and Absolute Values: A Generalization of London’s Conjecture
نویسنده
چکیده
We provide an inequality for absolute row and column sums of the powers of a complex matrix. This inequality generalizes several other inequalities. As a result, it provides an inequality that compares the absolute entry sum of the matrix powers to the sum of the powers of the absolute row/column sums. This provides a proof for a conjecture of London, which states that for all complex matrices A such that |A| is symmetric, we have sum (|A|) ≤ ∑n i=1 ri(|A|).
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تاریخ انتشار 2016