Re: matrices & polynomials in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg27277] Re: [mg27273] matrices & polynomials in mathematica*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sat, 17 Feb 2001 03:30:50 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Well, here is a function that shoudl do what you want: PolynomialMatrix[p_, x_][A_?MatrixQ] /; PolynomialQ[p, x] := Module[{u = CoefficientList[p, x], l, X}, l = Length[u]; u.(MatrixPower[X, #] & /@ Range[0, l - 1]) /. X -> A] For example, let p = 2 + 3x + 5x^2; A = {{1, 2}, {1, -2}}; then In[5]:= PolynomialMatrix[p, x][A] Out[5]= {{20, -4}, {-2, 26}} To see more clearly if this works let's try a case where we know what the answeris: In[6]:= p = Det[x*IdentityMatrix[2] - A] // Expand Out[6]= 2 -4 + x + x In[7]:= PolynomialMatrix[p, x][A] Out[7]= {{0, 0}, {0, 0}} So it seems to work. -- Andrzej Kozlowski Toyama International University JAPAN http://platon.c.u-tokyo.ac.jp/andrzej/ http://sigma.tuins.ac.jp/ on 01.2.16 5:58 PM, news.tue.nl at student at tue.nl wrote: > Hi, > > I have the following problem. > I have written a mathematica-module that automatically produces a certain > polynomial as a result. But I want another module to use this first module > and fill in a matrix in this polynomial. > for example: f[x]=1+x+x^2 > But when I compute f[A] where A is a matrix, mathematica interprets 1 as a > matrix filled with ones in stead of the identity-matrix. And A^2 is > pointswise multiplication in stead of matrix-multiplication. > Is there an option to let Mathematica know that the polynomial works on > matrices? > > Chris > > PS. I am aware of the possibility to multiply matrices using . (dot) but the > problem is that the polynomial is the result of some computations and I need > to have mathematica interpret this polynomial on matrices automatically. > > > > >