How Do You Apply Schmidt Orthogonalization to Four 4D Vectors?

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To apply Schmidt Orthogonalization to the four 4D vectors (1,1,-1,-1), (1,1,0,0), (1,2,3,1), and (0,1,0,1), start by setting u1 equal to the first vector. For each subsequent vector, subtract the projections of all previously computed u vectors from the current vector to obtain the next u vector. The projection is calculated using the formula proj(u_i)v_j = (dot(v_j, u_i) / dot(u_i, u_i)) * u_i. Normalize each u vector after computing it to ensure they are orthogonal and unit vectors. This process continues until all vectors have been processed, resulting in an orthogonal set.
haras
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Hello,
I must use this schmidt method to form an orthogonal set from the 4 column vectors: (1,1,-1,-1), (1,1,0,0,), (1,2,3,1), (0,1,0,1).
the only examples i can find are for 2 2space vectors, and that has the eqns.:
u1=v1
u2 = v2 - proj(u1) v2

i'm confused about how to expand that to 4 vectors in 4space, and also i think, about how to do projections.

THANKS!
 
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Do it step by step. After you have u1 and u2 do
u3=v3-proj(u1)v3-proj(u2)v3, and so on.
You should normallize the u's at each step.
 
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