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EDUğ %% 4th example of svd, April 16, 1999
EDUğ A=[2 2;1 1]

A =

     2     2
     1     1

EDUğ [u,s,v]=svd(A)

u =

    0.8944   -0.4472
    0.4472    0.8944


s =

    3.1623         0
         0         0


v =

    0.7071   -0.7071
    0.7071    0.7071

EDUğ A'*A

ans =

     5     5
     5     5

EDUğ [X,L]=eig(sym(A'*A))
 
X =
 
[ -1,  1]
[  1,  1]
 
 
L =
 
[  0,  0]
[  0, 10]

EDUğ s1=sqrt(10)

s1 =

    3.1623

EDUğ s2=0

s2 =

     0

EDUğ v1=[1 1]'/sqrt(2)

v1 =

    0.7071
    0.7071

EDUğ v2=[1 -1]'/sqrt(2)

v2 =

    0.7071
   -0.7071

EDUğ u1=(A*v1)/s1

u1 =

    0.8944
    0.4472

EDUğ cd A:\Tcodes

EDUğ nb=nulbasis(u1')

nb =

   -0.5000
    1.0000

EDUğ u2=grams(nb)

u2 =

   -0.4472
    0.8944

EDUğ U=[u1 u2]

U =

    0.8944   -0.4472
    0.4472    0.8944

EDUğ V=[v1 v2]

V =

    0.7071    0.7071
    0.7071   -0.7071

EDUğ S=[s1 0;0 0]

S =

    3.1623         0
         0         0

EDUğ U*S*(V')

ans =

    2.0000    2.0000
    1.0000    1.0000