Sunday, December 2, 2007

Linear Algaebra Section 4: Dot Products; Projection on a subspace; Least squares curve-fitting.

I had the most difficulty with example 4.4; I feel I may need a crash course in trigonometry! But I do appreciate the dot product is revisited later on in this class. But Least squares are very confusing, how can a single constant satisfy both equations that have no solution; is this approximation again? But if possible can we go over how to use the multiple of x and r (the residual vector) to determine the closest correct answer? also I would like to know what exactly the variables in this section represent; like what they are telling us about the vectors.

I suppose the idea of approximating solutions is better than no solution at all. As difficult as the calculations can be, they are useful. There are many situations that do not have an exact answer but approximations or the best educated guesses are the best available information we have.

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