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location Albany, CA
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visits member for 2 years, 6 months
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If I see further than most, it is because I have stood on the toes of giants and they kicked me high into the air...

However, there is nothing to suggest that I see further than most.

I am (inasmuch as one 'is' an occupation) an engineer. My mathematical skills are rather pedestrian, with a rare insight every now and then. I have been lucky enough to sit in the same room with some famous mathematicians & engineers. My Erdős number is 5, which undoubtedly makes me as unique as an Irishman in a pub. And I have been spotted in The Pub from time to time.

In professional circumstances, my value add has usually been the injection of common sense and completion of grunt work when perspectives and energies are unfocused.

My current age is the smallest number composed of the first two primes that would allow me to have watch on RTÉ the slightly contradictory small step for man and giant leap for mankind.

My real name is Joe Higgins. Apparently, my last name means 'of the Viking' in Irish.

My alma mater is University College, Cork in Ireland, and I had the additional privilege of obtaining my Phd. from the University of California at Berkeley under the enlightened tutelage of Lucien Polak.

I can be reached at joe dot higgins at gmail dot com.


1h
comment Borel Measures: Continuous vs. Discrete
Take the measure $\lambda+ \delta$.
1h
comment find median length when knowing the side length and its angle
$2L \cos \theta$.
3h
comment Prove that solutions to linear system form a vector space of dimension $\geq 2$
Does $B$ satisfy any conditions such as continuity?
4h
comment Finding a formula in terms of matrix elements of linear transformation
Of course it helps. $\|T\| = \max(|T(1)|,|T(-1)|)$ and you know that $T(-1) = -T(1)$ so the formula is $\|T\| = |T(1)|$. Compute $|T(1)|$ however you wish, it depends on the norm you are using.
4h
comment How to use MRUnit
How is this related to mathematics?
4h
comment Finding a formula in terms of matrix elements of linear transformation
How many points are there on the real line with $|x|=1$? And $T$ is linear, so that simplifies things.
5h
comment A problem on analytic function
Minor point: $D$ is not closed under the maps $z \mapsto z^2$, $z \mapsto z^3$. The constant function $f = 1$ eliminates one option...
5h
comment Probability of a coin falling on the edges of a square
It depends on how you interpret the sentence "Let a coin be randomly (and uniformly) dropped onto a square on the floor". This is Buffon sort of thing. It is good that you are asking such questions. Too few people think about the details.
21h
comment Rudin's Chapter 3: Numerical sequences and series
You are given a sequence of numbers $s_n$. Then $E$ contains all points $s$ such that there is a subsequence of $s_n$ that converges to $s$. If $s_n$ is unbounded above, then $+\infty \in E$, if it is unbounded below, then $-\infty \in E$. What is it about the definition that causes you doubt?
1d
comment In a Hilbert Space, if $\langle x,x_n \rangle \to 0$ then $\sup\{\|x_n\|:n=1,2,3,…\}<\infty$
Cauchy Schwartz gives $\|T_n x\| \le \|x_n\| \|x\|$, so $\|T_n \| \le \|x_n \|$. Then $T_n x_n = \|x_n\|^2$, which gives equality.
1d
comment In a Hilbert Space, if $\langle x,x_n \rangle \to 0$ then $\sup\{\|x_n\|:n=1,2,3,…\}<\infty$
Correct, I really meant to say that since the Baire category theorem was missing from your proof that something must not be right...
1d
comment In a Hilbert Space, if $\langle x,x_n \rangle \to 0$ then $\sup\{\|x_n\|:n=1,2,3,…\}<\infty$
The Banach Steinhaus is proved using the Baire category theorem...
1d
comment In a Hilbert Space, if $\langle x,x_n \rangle \to 0$ then $\sup\{\|x_n\|:n=1,2,3,…\}<\infty$
The Baire category theorem should feature in your proof...
1d
comment How to apply L'Hopital's rule to the limit of $\tan x/(1+\sin x)$ as $x\to 0$?
Both the numerator and denominator are continuous, and the denominator is non-zero at $x=0$, hence the limit is just the value of the function evaluated at $x=0$.
1d
comment Riemann Stieltjes Integral of discontinuous function
I don't understand your question.
2d
comment Find $\lim_{x\to\infty} \frac{e^{2x}-1}{e^{2x}+1}$ and $\lim_{x\to-\infty} \frac{e^{2x}-1}{e^{2x}+1}$
The second is straightforward just by continuity. The first can be rewritten as $1-{2 \over e^{2x}+1}$.
2d
comment Is $\|x\| = \| \overline{x} \|$ in an inner product space?
@alex.jordan: Good point, I have elaborated a bit.
2d
comment Does the dimension of the row space equal dimension of the column space for complex matrices?
As @DongRyulKim wrote, if $v_k$ form a basis of $\text{span}(A)$, then $\overline{v_k}$ form a basis of $\text{span}(\overline{A})$, so the dimensions of both spaces must be $k$.
2d
comment Making a complex inner product symmetric
I asked a related question here math.stackexchange.com/q/980510/27978.
2d
comment Making a complex inner product symmetric
By the way, it is not clear to me that the result is true in finite dimensions. You can always restrict to the subspace $\operatorname{sp} \{ x,y, \overline{x}, \overline{y} \}$ to prove the result for any pair $x,y$.