Revision as of 15:12, 21 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div> {{Alert-warning|This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion. }}Prove that for <math>H\in M_N(\pm1)</math> we have <math>|\det H|\leq N^{N/2}</math>, with equality precisely when <math>H</math> is Hadamard, in the sense that its rows are pairwise orthogonal.")
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Apr 21'25

Exercise

[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that for [math]H\in M_N(\pm1)[/math] we have [math]|\det H|\leq N^{N/2}[/math], with equality precisely when [math]H[/math] is Hadamard, in the sense that its rows are pairwise orthogonal.