Hadamard inequality

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For an LaTeX: n \times n matrix LaTeX: A,

LaTeX: 
\mbox{det} (A) \le \|A_{:,1} \| ... \|A_{:,n}\| = \prod_{j=1}^n \| A_{:,j} \|,
where LaTeX: A_{:,j} is the j-th column of LaTeX: A and norms are LaTeX: L_2.


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