
Re: Linear algebra equation solver?
Posted:
May 19, 2012 7:04 AM


Victor Eijkhout schrieb: > > I'm looking for software that can solve systems of linear algebra > equations. Example: > > I have two equations, z = y + ax (a scalar, x,y,z vector) & p^t z = 0 > (p another vector), assume no two vectors are orthogonal. Vectors > x,y,p are known, vector z and scalar a are unknown. > > The solution of this is z = y+az where a = (p^ta)^{1}(p^ty)
Actually it is z = y + a x where a = (p^t y) / (p^t x).
> > Is there software that can solve this sort of system of equations? >
You probably do not just mean solutions like this:
SOLVE([[z1, z2] = [y1, y2] + a*[x1, x2], [p1, p2]*[z1, z2] = 0], [a, z1, z2])
[a =  (p1*y1 + p2*y2)/(p1*x1 + p2*x2) AND z1 = p2*(x2*y1  x1*y2)/(p1*x1 + p2*x2) AND z2 = p1*(x1*y2  x2*y1)/(p1*x1 + p2*x2)]
SOLVE([[z1, z2, z3] = [y1, y2, y3] + a*[x1, x2, x3], [p1, p2, p3]*[z1, z2, z3] = 0], [a, z1, z2, z3])
[a =  (p1*y1 + p2*y2 + p3*y3)/(p1*x1 + p2*x2 + p3*x3) AND z1 =  (p2*(x1*y2  x2*y1) + p3*(x1*y3  x3*y1)) /(p1*x1 + p2*x2 + p3*x3) AND z2 = (p1*(x1*y2  x2*y1) + p3*(x3*y2  x2*y3)) /(p1*x1 + p2*x2 + p3*x3) AND z3 = (p1*(x1*y3  x3*y1) + p2*(x2*y3  x3*y2)) /(p1*x1 + p2*x2 + p3*x3)]
etc.
but the general solution for vectors of arbitrary dimension? Axiom or FriCAS may be the best candidate then.
Martin.

