most recent 30 from http://mathoverflow.net 2013-05-25T00:38:17Z http://mathoverflow.net/feeds/question/66493 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/66493/the-determinant-of-the-hadamard-product-of-two-matrices Anadim 2011-05-30T21:23:50Z 2011-05-30T21:23:50Z

<p>We know that the determinant of a Hadamard product of two positive semidefinite matrices $|{\bf A}\circ{\bf B}|$ is greater than or equal to $|{\bf A}||{\bf B}|$. Are there any general results on arbitrary matrices or something specific on other classes of matrices? </p> <p>I am specifically interested in the determinant of $|{\bf V}\circ {\bf R}|$ where the $i$-th row of ${\bf V}$ is $\left[x_1^{d_i} \;x_2^{d_i}\;\ldots \;x_N^{d_i}\right]$ and ${\bf R}$'s elements are all roots of unity.</p>