most recent 30 from http://mathoverflow.net 2013-05-22T19:55:02Z http://mathoverflow.net/feeds/question/94078 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94078/generalizing-the-spectral-radius-of-a-unistochastic-matrix Victor Liu 2012-04-15T00:47:08Z 2012-04-15T09:18:10Z

<p>Consider a square matrix $A$, and from it construct $B$ whose entries are the squared magnitudes of those in $A$. What can we say about the spectral radius of $B$? I know that for a unitary matrix $A$, $B$ is unistochastic so its spectral radius is 1, but I'm interested in the general case for arbitrary $A$.</p> <p>Also, relatedly, for general $A$, what can be said of the column 1-norms of $B$? And what about the the column 1-norms of products of such $B$-type matrices?</p>

http://mathoverflow.net/questions/94078/generalizing-the-spectral-radius-of-a-unistochastic-matrix/94094#94094 Felix Goldberg 2012-04-15T08:30:41Z 2012-04-15T09:18:10Z

<p>Well, $B$ is the Hadamard product of $A$ with itself, so if $A$ is nonnegative or psd, its radius is bounded from above by the square of the radius of $A$. </p> <p>For more information see this paper:</p> <p><a href="http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol20_pp90-94.pdf" rel="nofollow">http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol20_pp90-94.pdf</a></p>