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22h
comment Gradient of a dot product
It bears mentioning that the second formula works for any combination of dimensions, while the first works only when $a,b$ are $3$-vectors and you are taking the gradient with respect to a $3$-vector.
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awarded  Popular Question
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comment Pulling aces from a split deck
BTW I'm a programmer too, if you didn't learn about generating functions in Discrete Math you might want to read about them someday -- they're an incredibly powerful way of solving a lot of combinatorics problems.
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comment Pulling aces from a split deck
No worries, pick the answer most helpful to you!
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revised Pulling aces from a split deck
removed confusing references to Pathfinder
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answered Pulling aces from a split deck
Aug
24
comment Spectrum of matrix with single scaled row
Right, so can we perform some kind of decomposition on $M$ that will tell us how its spectrum changes, for any $a$? (Along the lines of the special case where the first row of $M$ is zero, except for $m_{11}$).
Aug
24
answered Simplifying $\frac1{gt}\sqrt{g/2h}\,dx$ in free fall equations
Aug
24
comment Simplifying $\frac1{gt}\sqrt{g/2h}\,dx$ in free fall equations
What is $dt/T$?
Aug
24
comment Spectrum of matrix with single scaled row
Well if you know anything about how the spectrum of $LD_aL^T$ changes as you change $a$ I'd be interested in that as well. My intuition is that knowing the Cholesky decomposition likely doesn't help you much, since computing it is "easy" while computing the spectral decomposition is "hard."
Aug
23
comment Prove or disprove that there exists a unique positive integer sequence $\{a_{n}\}$ satisfying a condition
Hmm, yeah it's not clear to me the sequence is unique...
Aug
23
comment verify $\lim_{x\rightarrow0}(4x^2+2x+5)=5$
Adriano has posted a direct proof above. One lesson to take away from this exercise is that proving general theorems, while sometimes more work up front, will then save you a lot of trouble later when you need to compute special cases!
Aug
23
answered verify $\lim_{x\rightarrow0}(4x^2+2x+5)=5$
Aug
23
comment An interesting math problem I created for an old-school RPG game.
Can potions push stats past the 25-point creation limit?
Aug
23
revised Finding eigenvectors for the largest eigenvalue vs one with the largest absolute value
added 55 characters in body
Aug
23
answered Finding eigenvectors for the largest eigenvalue vs one with the largest absolute value
Aug
21
answered A no regular curve.
Aug
19
awarded  Great Answer
Aug
18
asked Spectrum of matrix with single scaled row
Aug
2
comment Arc length inequality on ellipse
If $A$ satisfies the inequality for all $P,Q$ so does $A/2$, so there is no minimum value... the infimum of values satisfying the inequality is $A=0$.