most recent 30 from http://mathoverflow.net 2013-06-19T02:50:10Z http://mathoverflow.net/feeds/question/7934 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/7934/gradient-of-a-scalar-function-implying-a-rotor-equality-in-differential-systems Masi 2009-12-06T00:35:39Z 2009-12-06T00:35:39Z

<p><strong>How can the gradient of a scalar function (2x2 matrix) imply d(f1)/dx2 = d(f2)/dx1 ?</strong></p> <p>The only way how I can derive the equality is by considering the 2D matrix as a 3D one such that the curl gives you equality. However, I am unsure how a scalar function can imply the curl. </p>