SVD

Robert Israel — Thu, 10 Jun 2010 21:28:22 Z

Here's a 2 x 3 example:

> with(LinearAlgebra):
A:= evalf(<<1,2>|<-3,4>|<5,-6>>);
U,S,Vt:= SingularValues(A,output=['U','S','Vt']);
with(plottools): with(plots):
P1:= display([seq(arrow(Row(Vt,i),colour=red),i=1..3), 
                    sphere([0,0,0],1,style=patchnogrid,transparency=0.8), 
                    textplot3d([seq([1.1*Vt[i,1],1.1*Vt[i,2],1.1*Vt[i,3],v[i]],i=1..3)],colour=black)],
           scaling=constrained,axes=box,orientation=[-30,60]):
C:= cos(t)*S[1]*Column(U,1) + sin(t)*S[2]*Column(U,2):
theta:= arctan(U[2,1],U[1,1]):
P2:= display([
          seq(arrow(S[i]*Column(U,i),width=0.1,head_length=0.6,head_width=0.3),i=1..2),
          plottools[rotate](plottools[ellipse]([0,0],S[1],S[2],filled=true,colour=gray),theta),
          textplot([seq([(0.5+S[i])*U[1,i],(0.5+S[i])*U[2,i],s[i]*u[i]],i=1..2)])],
        scaling=constrained):
display(Array([P1,P2]));

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SVD