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wmboyles / Math-Summaries

Medium length summaries of math subjects like multivariable calculus. Longer than a formula sheet, shorter than a textbook.
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"Multivariable Calculus" section 6.2, 6.3. #22

Closed Suzukazole closed 3 years ago

Suzukazole commented 3 years ago

There seems to be an inconsistency in the use of \circ and \dot for representing dot products. Usually, \dot is used and it is better for this case, as \circ is used to represent tensor products.

wmboyles commented 3 years ago

Looking through 6.2 and 6.2, it looks like I tend to use \circ when taking the pullback, which is similar to function composition, hence the use of \circ.

I describe pullback and introduce the notation in 6.2 on the bottom of page 35: image

Meanwhile, I use \dot to represent dot products.

Here's an example in 6.2, page 37 that I think shows how each of the notations are used: image

As for \circ being use for tensor products, I've generally seen \otimes for them, while \circ is for function composition.

Suzukazole commented 3 years ago

Oh,that makes sense. I must have overlooked it while reading, my bad.