robjohn

West Hills, CA

none

Age: 55

the mean square The Mean Square
(with one standard deviation and several unusual ones)

aka Rob Johnson

$\LaTeX$ support for Chat

22m
comment Finding a matrix $X$ that changes the basis(?)
@Understand: the left side is just representing $\phi$ using the standard basis, that is $\phi(v)=vM$ for all $v$. The right side is writing $\phi(a)$ and $\phi(a')$ as combinations of $a$ and $a'$ or $\phi(b)$ and $\phi(b')$ as combinations of $b$ and $b'$. Then, a vector $$\begin{bmatrix}x&y\end{bmatrix} \begin{bmatrix}a\\a'\end{bmatrix}$$ is mapped to $$\begin{bmatrix}x&y\end{bmatrix} \begin{bmatrix}\phi(a)\\\phi(a')\end{bmatrix} =\begin{bmatrix}x&y\end{bmatrix} A\begin{bmatrix}a\\a'\end{bmatrix}$$
3h
comment Proof: Integral in between two bounds
Please don't change the question. People have taken the time to answer the first question; now their answers don't relate to the new question. If you have another problem, post another question.
10h
comment How to build generating function when there is restriction on number of occurrences
@Drupalist: yes, $\frac1{(1-x^2)(1-x)^2}$ is the generating function for the number of non-negative solutions to $2a+b+c=n$.
12h
answered Finding a matrix $X$ that changes the basis(?)
13h
revised Finding a matrix $X$ that changes the basis(?)
fix typo
14h
comment Finding the equation of the plane.
(+1) I was about to write an answer using $(-3,2,0)\times(-3,0,4)=(8,12,6)$, but this works just as well.
14h
revised How to build generating function when there is restriction on number of occurrences
fix typo and box generating function
15h
comment How to build generating function when there is restriction on number of occurrences
@VigneshManoharan: The coefficient of $x^{20}$ in $\frac1{(1-x^2)(1-x)^2}$ is $121$. However, in the unrestricted case, the coefficient of $x^{20}$ in $\frac1{(1-x)(1-x^2)(1-x^3)}$ is only $44$.
21h
answered Fourier Series estimation
21h
comment Proof: Integral in between two bounds
Try subtituting the bounds in for $\sqrt{1+x}$ in the integral.
21h
revised N-th roots equation
fix typo
21h
comment N-th roots equation
Shouldn't that be $1-n^{-c}=2^{-1/a}$?
22h
answered Binomial Theorem Help
22h
comment Binomial Theorem Help
This is definitely the way the hint suggests.
23h
comment How to take this integral? It looks like as Gamma but I'm confused.
Since the integral involves complex contours, I think that the shift to complex variables is necessary to justify the change of variables. If the function were not entire, problems can arise when the contour changes.
23h
comment How to take this integral? It looks like as Gamma but I'm confused.
(+1) I had written a similar answer, but yours was posted first.
1d
comment Show that if $f : \mathbb{R}^{2} \to \mathbb{R}$ continuously differetiable then $f$ is not inyective
You said you did not know topology and higher dimensional variants will probably require more topological tools.
1d
comment Euler-Lagrange Equation and "Eigen Value "
Is something missing? I see no $(1)$ or $(2)$.
1d
comment Show that if $f : \mathbb{R}^{2} \to \mathbb{R}$ continuously differetiable then $f$ is not inyective
@user162343: There is no theorem in multivariable calculus being used. The Intermediate Value Theorem is for single variable calculus. If you are interested in higher dimensional variants, you will probably need more topological tools.
1d
revised The fly and its owner
be more explicit
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