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Need help setting up a list of equations using "matrix notation"
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: Need help setting up a list of equations using "matrix notation"
*From*: jmm at umich.edu
*Date*: Wed, 6 Jul 1994 13:25:52 -0700 (PDT)
I am trying to set up a model to solve a system of equations. There are three
different types of equations. For clarity and generality I want to express
each equation type in "matrix notation", that is, as x == y, where x and y are
both column vectors. Thus, I think I want to represent the following
{ {x1 == y1}, {x2 == y2}, . . . , {xn == yn}}
in compact matrix notation.
I am not succeeding. When I try to put together the 3 sets of equations (say,
to feed to FindRoot), I am getting a mess. Here is a sample of how I try it.
(rho and dL are 2x1 vectors; mu is 3x1; dZ is 3x2. Through the magic of
Mathematica's matrix algebra, Dot[mu,dZ] or mu . dZ is 2x1)
In[140]:=
prices = rho - (gamma * (1 + dL) +
(mu . dZ)) == ZeroMatrix[2,1]
Out[140]=
-200 + g1 -2200 + g2 mu1 mu2
{-(gamma (1 + --------- + ----------)) - --- + --- +
18750 37500 3 3
2 mu3
----- + rho1, -(gamma
3
-200 + g1 -2200 + g2 mu1 2 mu2
(1 + --------- + ----------)) + --- + ----- +
37500 18750 3 3
mu3
--- + rho2} == {{0}, {0}}
3
So, if x and y are 2x1 vectors, I am basically get the following list:
{{x1,x2} == {y1,y2}} (type A)
When I need something in the form
{{x1 == y1}, {x2 == y2}}. (type B)
Obviously, I am not a wizard at list processing. Can someone point me towards
a clean, elegant way to set up this vector of equations so that I can still
use matrix notation and end up with an equation list (of type B) that I can
combine with another equation list? (Alternative, a way to combine two lists
of type A to make a single list that FindRoot would be happy with?)
--
Prof. Jeff MacKie-Mason
Dept. of Economics Jan-July 28 '94: California Energy Institute
Univ. of Michigan 2539 Channing Way
Ann Arbor, MI 48109-1220 Berkeley, CA 94720
internet: jmm at umich.edu phone: 510-642-3570 fax: 510-642-3570
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