Simplification in chapter 9.5 #201

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JeffreyFalgout opened this Issue Dec 14, 2015 · 2 comments

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@JeffreyFalgout

Formula 9.37 is
image

The image term can be simplified to a dot product between alpha and the 1 vector. Since the transpose notation hasn't been used anywhere else in the book as far as I can tell, I think it would make more sense to stick with dot products.

@Kkevsterrr

The transpose notation is used liberally in later sections (see section 13), so if it isn't explicitly defined in 9 (or wherever it first appears), it might be good to define it. But for accuracy of the equation, it should stay.

@JeffreyFalgout

From the point of view of this book being used for CMSC422:

I feel that one of the biggest barriers in 422 is that most CS students don't quite have enough math for the course. a • b, ⟨a, b⟩, and aTb all define the same operation in Euclidean space, but most students probably haven't seen inner products/transpose notation since MATH240 (if at all). I think it would be a good idea to use dot products (including later in the book) where possible to keep the cognitive load as small as possible.

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