Perhaps it would be helpful to first solve this problem for n=3. Consider a cubic equation. The roots of the derivative quadratic are the foci of the inellipse of the triangle formed by the roots of the cubic (in the complex plane). This is the Siebeck-Marden theorem: https://en.wikipedia.org/wiki/Marden%27s_theorem The line through the foci of the inellipse is the least-squares approximation line through the roots of the cubic. So you're doing a flavor of "principle component analysis" https://en.wikipedia.org/wiki/Principal_component_analysis At 09:36 AM 10/15/2015, Mike Stay wrote:

What operation on a matrix M gives a new matrix M' whose characteristic polynomial is the derivative of the char. poly. of M? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com