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Jan
28
comment Help reading a scatterplot
Without more info. I would say that it is hard to infer much other than more lines more bugs. How do you associate a bug with a particular number of lines, how mature is the code, do the bugs arise from a particularly delicate piece of code, etc, etc. It really depends on context.
Jan
28
comment Is it a subspace or not?
The reason that the first one works is that $x \mapsto x^3$ is injective on the reals, so $a^3 = b^3$ iff $a=b$. This suggests a possible way to obtain a counterexample.
Jan
28
answered Prove that $az^n+b\overline{z}^n=0$ does not have any complex solutions except for $0$
Jan
28
comment Help reading a scatterplot
It really depends on context, but assuming this is homework, I would say that here is a strong linear relationship and the ringed point is an outlier. However, in real life, one should take a good look at outliers, especially one that is 'way off'.
Jan
28
comment Math and geometry software to create instructional videos
Your intended sarcasm is hardly concomitant with the wording of the question...
Jan
28
comment Math and geometry software to create instructional videos
Then it is a professional endeavour. And people get paid consulting fees.
Jan
28
answered Is the function complex differentiable at (0,0)?
Jan
28
comment Limits and derivatives - limit of a trigonometric function
Roughly $\sin x \approx x$ for small $x$. So you should expect $x^8$.
Jan
28
comment Math and geometry software to create instructional videos
I don't understand the 'amateur project' and 'to gain a profit'? Which is it? One is a reasonable question here, the other is a shopping suggestion which is not.
Jan
28
answered Is the rank of a matrix unaffected by congruence transformations?
Jan
28
comment Binary to Decimal Floating Point Number
Let $b_n b_{n-1} \cdots b_0$ be the binary digits (zero or one), then the number is $\sum_{k=0}^n b_k 2^k$.
Jan
28
comment Product of matrices of a linear operator and of its inverse
What does multiplication mean here? $\phi(x), \phi^{-1}(x)$ are elements of a vector space?
Jan
28
comment ${f \text{ is differentiable on } I \iff f_{\left|\ [a,b]\right.} \text{ is differentiable }\ \forall a,b \in I}$
For the other direction, note that $I = \cup_{a,b \in I} [a,b]$.
Jan
28
comment Relationship between supremum of the partial derivative and the derivative of the supremum
Is $\| F( \cdot, t) \|_\infty$ differentiable with respect to $t$???
Jan
28
answered How do I prove this statement about the operator norm?
Jan
28
answered How to bound the biggest eigenvalue of $\sum_{i=1}^{n}x_ix_i^T$?
Jan
28
comment How do I prove this statement about the operator norm?
What is a Fourier ensemble? It this a finite dimensional problem?
Jan
28
comment Theorem about equivalent norms.
This can't be true. Just compare the equivalent norms $\|\cdot\|_1$ and $\|\cdot\|_\infty$ on the point $(1,1)$.
Jan
28
comment How do I prove this statement about the operator norm?
It is not true. If you take $A=-I$, then $\|A-I\| = 2$, but the rightmost term will be zero.
Jan
28
comment Let $X_1,X_2\sim N(0,1)$. How to find joint pdf of $\,Y_1=X_1^2+X_2^2\,$ and$\,\,Y_2=X_1/\sqrt{Y_1}$?
Are the $X_k$ independent?