range=orth(a)
Inputs  
a 
Any matrix. 
Outputs  
range 
A matrix containing the basis for the colums of a , that is, for any vector x , a*x can be
written as a linear combination of the columns of range .

null space
of any matrix (obtained by calling the function null
) is orthogonal
to the range of its transpose.
>>a=[2 3 4;5 6 7] >>b=orth(a') // b is the range of a' >>b 0.4767 0.7785 0.5721 0.0778 0.6674 0.6228 >>c=null(a) >>c 0.4082 0.8165 0.4082 >>a*c // c is the null space of a Scaled by 10^15 0.4441 0 >>c'*b // columns of c and b are orthogonal. Scaled by 10^16 0 2.2204