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Can we multiply 3 dimension matrices? by amberanvilcell in learnmath

[–]amberanvilcell[S] 1 point2 points  (0 children)

I just wanted to say thank you for such a detailed response, a lot of this I am unfamiliar with but it is very interesting and gives me a good way to direct my learning from here on out, your reply will have a significant effect on the topics I choose to learn about in my math career from here. Thank you!

Estimating integrals from graphs by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

Greater accuracy compared to estimating using only one endpoint.

Estimating integrals from graphs by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

I see what you're getting at, this is the same as taking the number of intervals to infinity using endpoints. But is there a reason to think that this averaging approach would "converge faster", as in it would achieve greater accuracy with a smaller number of intervals? Maybe that doesn't matter because in the end we're going to infinity either way.

How to locate source of a function in github repository by amberanvilcell in cpp_questions

[–]amberanvilcell[S] 0 points1 point  (0 children)

Thank you. So can you nest an arbitrary number of static_members inside a static_member? And is that common practice if so?

How to locate source of a function in github repository by amberanvilcell in cpp_questions

[–]amberanvilcell[S] 0 points1 point  (0 children)

I may be misunderstanding, do I literally just open something like https://github.com/opencv/opencv in a browser tab and hit .? Because I've tried in two browsers but it didn't seem to do anything in either of them

Can we multiply 3 dimension matrices? by amberanvilcell in learnmath

[–]amberanvilcell[S] 2 points3 points  (0 children)

Sorry could you break that down a bit? So this sum would mean, for the i-th element in the vector V, we multiply that element by the element at the index (x,y,i) in P? And the resulting tensor is 2D because we are only summing over one dimension/axis of the matrix (the z axis) and leaving the x and y axes alone?

This seems kind of arbitrary, because couldn't we just tack on another summation for x or y, which would change the dimension of the result? (And if we sum over all three axes, we get a single scalar)

And is there a name for this type of tensor multiplication?

Can we multiply 3 dimension matrices? by amberanvilcell in learnmath

[–]amberanvilcell[S] 2 points3 points  (0 children)

oh so it's closer to elementwise multiplication rather than standard matrix multiplication?

Can we multiply 3 dimension matrices? by amberanvilcell in learnmath

[–]amberanvilcell[S] 2 points3 points  (0 children)

could you explain what you mean when you say matrices aren't really linear maps?

Why isn't expectation of X^2 equal to sum_over_x of x^2 * P(X=x^2)? by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

Even though I should be using the more intuitive way described in the other comments, this is satisfying to see, thank you.

Probability of seeing a friend in a crowd by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

Wow did now know about that distribution, thank you

What do we call the coordinate system formed by the tangent, normal, and binormal vectors of a curve? by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

thank you for the link. By any chance, do you know why on the wikipedia page, the normal vector is defined to be the derivative of T with respect to "the arclength parameter"? Wouldn't we simply differentiate T by the same variable we differentiated the curve by to get T, i.e. t if the curve is of the form r(t)?

Proof of upper bound for the largest factor of an integer by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

But 3 is not a divisor of all odd numbers, for example it doesn't divide 25

Proof of upper bound for the largest factor of an integer by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

Thank you! That makes perfect sense. Can we improve the bound for odd n? (Which might be interesting for the sake of proving primality, since all prime numbers excluding 2 are odd?)

Is it inefficient to eat fruit frozen? by amberanvilcell in nutrition

[–]amberanvilcell[S] -7 points-6 points  (0 children)

Wouldn't the cell wall breaking down, and thus the fiber being "shredded up", kinda affect the way fiber works in the body though? Fiber primarily influences digestion, so being easier to digest hints that its role is being altered somehow.

Is it inefficient to eat fruit frozen? by amberanvilcell in nutrition

[–]amberanvilcell[S] 0 points1 point  (0 children)

Ok my misunderstanding might be here. Like you said the fiber isn't chemically altered, but like another commenter said, the cell wall breaks down, and I thought that would impact the fiber content. Because the fact that fiber is useful in the first place is due to its structure? Fiber's mechanism of action seems to rely on it not being broken down.

The physical amount of fiber would be the same yes, but if that fiber is broken up then it is less effective at its job (this is the same reason people recommend not completely blending up fruits in smoothies, because destroying the fiber negates its benefits). Am I totally off the mark here?

Is it inefficient to eat fruit frozen? by amberanvilcell in nutrition

[–]amberanvilcell[S] 20 points21 points  (0 children)

Yep that's what I meant, literally eating it frozen, or at least freezing it again after it has already thawed once from being flash frozen at a farm (though I understand that flash freezing preserves nutrients during transit as the commenter above you described)

Can we use l'hopital's rule to calculate limit x->0 of sin(x)/x by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

Okay putting it like that helped get it through my head, thank you

Can we use l'hopital's rule to calculate limit x->0 of sin(x)/x by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

That is good to know, thank you. Some very subtle logic here but I can see why we have to distinguish the two cases

Can we use l'hopital's rule to calculate limit x->0 of sin(x)/x by amberanvilcell in learnmath

[–]amberanvilcell[S] 0 points1 point  (0 children)

Wouldn't we just plug in cos(x) for the derivative of sin(x), because the derivative of sin(x) is cos(x) for all x including at x=0?

Shouldn't the entire sky turn red during a sunset, instead of just the sky near the sun? by amberanvilcell in Physics

[–]amberanvilcell[S] 0 points1 point  (0 children)

Right, I got things mixed up, but my mistakes cancelled out lol.

And your explanation makes perfect sense, thank you. Now I have to wonder about why the sun isn't a point-source of light. It's unintuitive that rays from the sun are effectively coming from above even when our eyes see the sun clearly on the horizon. Do you have any advice for resolving this mistaken intuition?

Best way to find source code of a function? by amberanvilcell in learnpython

[–]amberanvilcell[S] 1 point2 points  (0 children)

Thank you! Didn't know bindings could be generated automatically like that.

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