Gene's answer suggests the question of whether there exists a continuous mapping f: M_n[C] —> M_(n-1)[C] from n x n matrices over the complexes C to (n-1)x(n-1) matrices over C such that in C[t], (d/dt)charpoly(M)(t) = charpoly(f(M))(t) for all M in M_n[C]. —Dan
On Oct 15, 2015, at 12:26 PM, Mike Stay <metaweta@gmail.com> wrote:
On Thu, Oct 15, 2015 at 2:59 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com>> wrote:
Solve for the roots of the derivative polynomial. These are the eigenvalues of M'. String them along the diagonal, and make an arbitrary similarity transformation. If M' has repeated eigenvalues, Jordan blocks are also possible.
From: Mike Stay <metaweta@gmail.com <mailto:metaweta@gmail.com>> To: math-fun <math-fun@mailman.xmission.com <mailto:math-fun@mailman.xmission.com>> Sent: Thursday, October 15, 2015 9:36 AM Subject: [math-fun] Characteristic polynomial question
What operation on a matrix M gives a new matrix M' whose characteristic polynomial is the derivative of the char. poly. of M?