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Dec
11
awarded  Caucus
Dec
8
comment how to solve a linear equation with two variables?
You do not have enough information to solve for both variables at the same time. You can write $$J=\frac{M}{\omega}+\frac{K}{\omega^2},$$ or $$K=\omega^2 J-\omega M.$$
Dec
1
comment How to prove that nth differences of a sequence of nth powers would be a sequence of n!
You should try to build a theory of "discrete differential and integral calculi" where real valued functions are replaced with sequences, the derivative is replaced with the difference operator, and the integral is replace with the summation operator. You even get an analog of the fundamental theorem of calculus.
Nov
30
comment Mean of standard deviation and confidence intervals
Here is a way you can test this. Pick two random samples of size say ten (instead of 1000), between zero and one. Calculate the mean and standard deviations of the two examples. Then calculate the mean and standard deviation of the two samples combine and compare.
Nov
26
comment meaning of principal eigenvector of the normalized link matrix (pagerank)
What you want to imagine is that each node has some amount of "material". At each time step, the material from each node is distributed to all of the other nodes in a way that is specified by the weighted adjacency matrix. The dominant Eigenvector then is the distribution you get after an infinite number of time steps.
Oct
19
comment Why can't a Venn diagram constitute a proof?
It seems like you can use Venn diagrams to prove statements about subsets of $\mathbb{R}^2$
Oct
19
comment Find the minimum capacity edge that is maximized among all paths from $s$ to $t$
Their are some subtleties to this. The first step is to find all the paths from $s$ to $t$, which could be infinite in number, if you graph has loops. So you would probably restrict paths that do not circle around. One you have that, it seems to me that this is a relatively straight forward search.
Oct
19
comment What are the continuous functions that satisfy the following?
The word continuous in this case is simply an adjective you have to carry around with you during the argument. This might seem counterintuitive, but it is due to the fact that $\mathbb{R}-\{0\}$ is disconnected.
Oct
19
comment What are the continuous functions that satisfy the following?
Minor nitpick: Based on the question, it does not seem that the question needs to be defined at zero. Of course, this does not change the character of the solution method.
Oct
18
comment Is there a basis for the continuous functions space?
@Hayden I think that in analysis, one uses a slightly different notion of basis. Analysts often do not deal with "naked" vector spaces, but topological vector spaces. So one might call these "topological" bases.
Oct
18
comment A function having limit at every point but continuous nowhere
@YiorgosS.Smyrlis I figured that. My "axiom of choice" alarm went off.
Oct
18
comment A function having limit at every point but continuous nowhere
One wonders what happens if one has a model of set theory such that "a countable union of a countable sets is countable" is false.
Oct
18
comment A function having limit at every point but continuous nowhere
If there is such a function, it seems quite weird.
Oct
8
comment Understanding matrices.
What makes a matrix a matrix is that one can and should multiply them. Multiplication naturally corresponds to composing the linear maps functions. If you care about efficiency here, the matrix data structure may not be entirely appropriate. Multiplying two 2x2 matrices requires eight multiplications, four additions and in your case two trig evaluations. Here you could get by with three (one to add the angles, two for the two equations) additions and two trig evaluations.
Oct
5
comment Linear regression using gradient descent in Octave seems to fail
I imagine from the looks of your graph, that you are doing gradient decent on SOMETHING.
Sep
30
awarded  Explainer
Sep
25
awarded  Nice Question
Sep
24
awarded  Autobiographer
Sep
16
comment Using Big-O to analyze an algorithm's effectiveness
By the way, en.wikipedia.org/wiki/Big_O_notation#Orders_of_common_functions might be helpful in general.
Aug
23
comment Canonical Map in a Category with Finite Products, Coproducts and a Zero Object.
I must say, they are indeed nice pictures.