929 reputation
1820
bio website wolfram.com
location United States
age 37
visits member for 4 years, 2 months
seen 12 hours ago

The gravatar was made with Mathematica, and inspired by this.

The contents of my posts are my own opinion, and do not reflect the opinions of my employer.


Jun
3
revised Inverting the sum of a Dense and Diagonal matrix
added response to second part
Jun
2
revised Inverting the sum of a Dense and Diagonal matrix
added link to review article
Jun
2
answered Inverting the sum of a Dense and Diagonal matrix
Jun
1
comment Integration of a first order ODE
just from looking at it, it is obvious that $y(t)=ce^{5t}$ is a solution. But, what I've always struggled with is, is there a systematic way of choosing the particular solution? My issue is it seems odd that we can systematically, for the most part, find the homogenous solution, yet in finding the particular solution, we are reduced to guessing. Yes, they're educated guesses, but there is still an element trial and error that is bothersome to me.
May
24
answered A series solution of the differential equation: $\frac{d^2u(x)}{dx^2}+ u(x)^n = 0.$
Apr
20
revised What is the signature of a matrix?
fixed notation
Apr
20
suggested approved edit on What is the signature of a matrix?
Apr
19
awarded  Enthusiast
Apr
18
comment On maximizing a function
A few questions: is $n$ real or is it an integer? what do you know about $b$? what about $q_i$? what is the range on your sum? The reason I ask, is that if your sum range is small and n is an integer (with a small $N$), then if may be easiest just to calculate every possible value.
Apr
18
comment Spectrum of a linear operator
question on notation, does your statement $\theta \in ]0,1[$ mean that the set is non-inclusive?
Apr
18
answered Why this spectrum problem is self-adjoint?
Apr
18
comment Why this spectrum problem is self-adjoint?
This has me confused, and I believe your notation is a hindrance. Let the dagger, $\dagger$, denote the conjugate-transpose, or adjoint, i.e. $A^\dagger = (A^\ast)^T$, where $\ast$ denotes complex conjugation. Now, if $M$ is Hermitian (or, self-adjoint), then $M^\dagger = M$. This implies that the diagonal of $M$ must be real, so $k = i c$ where $c \in \mathbb{R}$. Then your eigenvalues are $\pm \sqrt{c^2 + |q(x)|^2}$. So, with the notation changes could you clarify why your confused?
Apr
16
revised Parallel Projection Of An Ellipse
formatted equations
Apr
16
suggested approved edit on Parallel Projection Of An Ellipse
Apr
12
accepted Under what conditions is integrating over a series expansion valid for an improper integral?
Apr
12
revised Under what conditions is integrating over a series expansion valid for an improper integral?
reverted
Apr
10
comment Under what conditions is integrating over a series expansion valid for an improper integral?
We determined that the pole at the origin was the cause of the problem. But, I also found that if the integration limits each corresponded to a pole, i.e. $x \in [\pi(n-1), \pi n]$, you are unable to compensate for the pole. But, if you shifted the integral to $x \in [\pi(n - 1/2), \pi (n + 1/2)]$ the poles can be compensated for, and the series of integrals is an alternating series, $i \sum (-1/e)^n$, which converges to $-i/(1-e)$.
Apr
10
revised Under what conditions is integrating over a series expansion valid for an improper integral?
added addt'l request from the community
Apr
10
comment Under what conditions is integrating over a series expansion valid for an improper integral?
@JM, I have no idea, but it did bring up some questions on how to proceed.
Apr
8
awarded  Nice Question