The Gram-Schmidt Process

The primary friction point often lies in distinguishing between the original vectors

v_i

and the newly constructed orthogonal vectors

u_i

within the summation. Students frequently substitute

v_i

for

u_i

in the denominator or sum. Remember,

u_j

is made orthogonal to *all previously constructed orthogonal vectors*

u_1, ..., u_{j-1}

, not the original

v_i

Institutional Reference: Linear Mathematics