Hi I already know the "usual" Gram-Schmidt Process: But, then I discovered another Gram-Schmidt process that gives an orthogonal basis (in Matrices and Linear transformations by Charles Cullen): Essentially, it is the same except you do not divide by <uj,uj>. Cullen calls this the Gram-Schmidt process, yet it is different. Does it give a different basis? The explanations for the usual Gram-Schmidt process are usually visual while the explanation for this one was algebraic. I cannot make sense of it in any of the visual explanations of the Gram-Schmidt process, yet it makes perfect sense algebraically; How are these processes different? Or, if they aren't, why?