Gram-Schmidt takes a set of vectors and makes the column vectors
normal to each other,

Here is an example for a 3 by 3 vector

Assume a matrix called xx is

| 2  3  4 |
| 5  6  7 |
| 4  5  3 |

Select desired vector n= 1,2,3

gs()
Prgm
ClIO

rowDim(xx)->rd
SubMat(xx,1,1,rd,1)->v1
SubMat(xx,1,2,rd,2)->v2
SubMat(xx,1,3,rd,3)->v3

If n=1 Then
  Disp n,v1
EndIf

If n=2 Then
 v2-dotP(v2,v1)/(dotP(v1,v1))*v1->ou 
 Disp n,ou
EndIf

If n=3 Then
 v2-dotP(v2,v1)/(dotP(v1,v1))*v1->v2
 v3-dotP(v3,v1)/(dotP(v1,v1))*v1-dotP(v3,v2)/(dotP(v2,v2))*v2
  ->ou
  Disp n,ou
EndIf

EndPrgm

       | 2 |             |   .5111   |          | .6428   |
v1= | 5 |     v2 = |   -.2222  |   v3 = | 1.2857 |
       | 4 |             |   .02222 |          | -1.928  |

If a unit vector is desired, use unitV(  )