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3. Numerical Linear Algebra 103

5.4 M-file for Gram-Schmidt Orthogonalization
Procedure

gramgv.m

%Given the independent vectors as the input,Orthonormal vectors as the
%output computed using Gram-Schmidt Orthogonalization procedure
%Input vectors are arranged rowwise

function [res]=gramgv(x)

o{1}=x(1,:)/sqrt(sum(x(1,:).^2));
for k=2:1:size(x,1)
s=x(k,:);
for m=1:1:k-1
s=s - ((o{m}*x(k,:)')/(o{m}*o{m}'))*o{m} ;
end
o{k}=s/sqrt(sum(s.^2));
end
res=o;

6. COMPUTATION OF THE POWERS
OF THE MATRIX ‘A’

Consider the matrix A = 3 4 . The matrix A 100 is computed as

1 2

described below.

The matrix ‘A’ can be diagonalized using eigen matrix ‘E’ (every column
vector is the eigen vector of the matrix ‘A’) as described in the section 3