Re: Matrix Form of Quadratic Equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg114243] Re: Matrix Form of Quadratic Equations*From*: Simon <simonjtyler at gmail.com>*Date*: Sun, 28 Nov 2010 06:54:57 -0500 (EST)*References*: <ico2b2$nq6$1@smc.vnet.net>

On Nov 26, 6:32 pm, Ari <ari... at finly.net> wrote: > Hello, > > Could anyone guide me how to build a mathematica module to form a Matrix = form from a quadratic equations? > For example, x^2 + y^2 - 2 x y will output > {{1, -1}, {-1, 1}} ? > > Thanks Hi there, I was sure that you would be inundated with answers... but none arrived. So here's my quick answer. Define quad: In[1]:= quad = a x^2+b x y+c y^2; Then either calculate the Hessian (http://mathworld.wolfram.com/ Hessian.html) In[2]:= 1/2D[quad,{{x,y},2}] {x,y}.%.{x,y}==quad//Expand Out[2]= {{a,b/2},{b/2,c}} Out[3]= True Or extract the coefficients using CoefficientList[] In[4]:= CoefficientList[quad,{x,y}] Extract[%,1+{{2,0},{1,1},{0,2}}] {x^2,x y, y^2}.%==quad Out[4]= {{0,0,c},{0,b,0},{a,0,0}} Out[5]= {a,b,c} Out[6]= True In terms of how to "build a mathematica module to form a Matrix form from a quadratic equations", it's probably good to use a general approach like Hessian[f_, x_List?VectorQ] := D[f, {x, 2}] Hessian[f_, x_List?VectorQ, x0_List?VectorQ] /; Length[x] === Length[x0] := Hessian[f, x] /. Thread[x -> x0] Hessian[f_, x_List?VectorQ, x0_?NumericQ] := Hessian[f, x] /. Thread[x -> x0] Simon