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Projection using Modified Gram-Schmidt orthogonality

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I need the Modified Gram-Schmidt orthogonalization method in my Research.
I wrote the following code for the projection using the Classic Gram-Schmidt:
function[Xp] = Project(A,B)
Xp = [] ;
u1 = B;
for i = 1:1:6
u2 = A(i,:)- (A(i,:)*u1)/(u1'*u1) * u1';
Xp = [Xp;u2] ;
I faced problems to convert the Modified Gram-Schmidt orthogonalization method into MATLAB code, which is illustrated in the following link
under section Numerical stability.
Can anyone help me in this problem please?
Torsten on 26 Jan 2023
Then I can assure you that from what you wrote, nobody will be able to understand what you are looking for.
Try to understand the problem first before looking for a solution.
Jan on 28 Jan 2023
@M: Please stop addressing specific users by messages like "Hi @xyz do you have any idea about my question please?"
Imagine what would happen, if all users do this: The most active users would receive a huge number of notifications and find less time to post answers.

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Accepted Answer

Matt J
Matt J on 25 Jan 2023
Edited: Matt J on 26 Jan 2023
Aorth=orth(A); %A orthogonalized
ProjB=Aorth*(Aorth.'*B); %projection of B
Torsten on 26 Jan 2023
I'm surprised you now found what you were searching for.
In the end, was it projecting a single vector onto a set of vectors or a set of vectors onto a single vector you were aiming at ?
M on 26 Jan 2023
@Torsten, my problem is an optimization problem. it contains equations and I need to know unknown values using several orthogonal techniques. Thanks

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