\C-flows A^z of linear maps A expressed in terms of A^{-1},A^{-2},...,A^{-n} and analytic functions of z

Details \C-flows A^z of linear maps A expressed in terms of A^{-1},A^{-2},...,A^{-n} and analytic functions of z \C-flows A^z of linear maps A expressed in terms of A^{-1},A^{-2},...,A^{-n} and analytic functions of z

2007-06-28

arxiv.org/abs/0706.4177v1

Mathematics

Commutative Algebra

Scientific paper

Suppose A\in GL_n(\C) has a relation A^p=c_{p-1}A^{p-1}+.... + c_1 A+ c_0I where the c_i in \C. This article describes how to construct analytic functions c_i(z) such that A^z=c_{p-1}(z)A^{p-1}+... + c_1(z) A+ c_0(z)I . One of the theorems gives a possible description of the c_i(z): c_i(z)=C^z\alpha where C\in Mat_p(\C) is (similar to) the companion matrix of X^p-c_{p-1}X^{p-1}-... -c_1X-c_0I, and \alpha:= (c_{p-1},...,c_1,c_0)^t.

Affiliated with

Also associated with

No associations

Rating

\C-flows A^z of linear maps A expressed in terms of A^{-1},A^{-2},...,A^{-n} and analytic functions of z does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with \C-flows A^z of linear maps A expressed in terms of A^{-1},A^{-2},...,A^{-n} and analytic functions of z, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and \C-flows A^z of linear maps A expressed in terms of A^{-1},A^{-2},...,A^{-n} and analytic functions of z will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-456421