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Topic: Linear algebra equation solver?
Replies: 3   Last Post: Nov 25, 2012 5:15 AM

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clicliclic@freenet.de

Posts: 983
Registered: 4/26/08
Re: Linear algebra equation solver?
Posted: May 19, 2012 7:04 AM
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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.



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