Given m x n matrix X

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STEP 1 (classical and modified)

q   = X(:,1)
r11 = norm(q)
q1  = q/r11 







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STEP 2 (classical and modified)

q   = X(:,2)
r12 = q1'*q
q   = q - r12*q1
r22 = norm(q)
q2  = q/r22







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STEP 3 - CLASSICAL 

q   = X(:,3)
r13 = q1'*q;   r23 = q2'*q;
q   = q - r13*q1 - r23*q2
r33 = norm(q) 
q3  = q/r33






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STEP 3 - MODIFIED

q = X(:,3)
r13 = q1'*q;
q   = q - r13*q1;
r23 = q2'*q;
q   = q - r23*q2;
r33 = norm(q) 
q3  = q/r33

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