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- Title:
Inequalities for Matrix Powers and Absolute Values: A Generalization of London’s Conjecture
- Author(s):
- Hanjo Täubig
- Abstract:
- 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 $sum(|A^p|) \le \sum_{i=1}^n r_i(|A|)^p$.
- Keywords:
- inequalities, matrix powers, absolute values
- Year:
- 2016
- Language:
- en
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