64,151 reputation
22881
bio website
location Albany, CA
age
visits member for 2 years, 8 months
seen 2 hours ago

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.


2h
comment Solving eqn. of the form K = AGL + BGT, where A,B,L,T are invertible matrices.
There's a lot of stuff out there, its impossible to keep abreast of everything...
2h
comment Help with a 3-body problem
The one body I have requires a lot of maintenance...
8h
comment Proof If $A_{2x2}$ and $\lambda$ real number then $|\lambda I-A|=\lambda^2-(\operatorname{tr}A) \lambda+|A|$
Subtract the two terms and see if the result is zero.
9h
comment Are normed spaces isodyne?
Not offhand. It is not true in general metric spaces, of course. Take $(0,1) \cup \{2\}$ with the usual $\mathbb{R}$ metric. Then $\{2\}$ and $(0,1)$ are open but do not have the same cardinality.
10h
comment Is a linear operator applied to itself still linear?
Take a polynomial $p$, then the operator $p(A)$ is also linear.
10h
comment A question on Terence Tao's representation of Peano Axioms
I don't have the book so there may be more context that I am missing, but I think he is focusing on the "can be obtained from" part, because it doesn't eliminate 0.5 as you note.
11h
comment Finding non-zero eigenvalues of a $5\times 5$ matrix
Consider the behaviour on the subspaces spanned by $e_1,e_5$ and its orthogonal complement.
19h
comment Prove an upper bound for the determinant of a matrix A
You show that in the $3 \times 3$ case that $\det A \le 3$. Shouldn't you show that it is $\le 2$?
19h
comment How does the author apply the implicit function theorem?
The difference is that I am using explicit coordinates whereas the proof above uses subspaces of corresponding dimensions. In the expression $f(p+x+y)$, the point $p \in \mathbb{R}^k$ satisfies $f(p)= 0$, and we have $x \in X, y \in Y$. We have $\dim X = \dim \ker {\partial f(p) \over \partial x} = m$ and $\dim Y = k-m$. The $h$ you have above is a map $h : X \times Y \to \mathbb{R}^{k-m}$.
22h
comment How does the author apply the implicit function theorem?
Its a more complicated way of doing what I did.
23h
comment How to create a computationally cheap function passing through given points?
The function $f(x) = \sqrt[3]{10^{10} \over 2.3x-80218}$ is a reasonable (visual) fit to the data.
23h
comment How to create a computationally cheap function passing through given points?
If you plot $(x,{1 \over y^3})$ instead of $(x,y)$ you get a moderately straight line.
23h
comment How to create a computationally cheap function passing through given points?
Are you trying to compute the interpolating function in real time or just evaluating the function?
23h
comment What is meant by $AB$ in boolean algebra?
No, just a way of 'getting around' the minimum number of characters in a comment. Not much point really, as it requires typing more. Just because I can :-).
23h
comment What is meant by $AB$ in boolean algebra?
No worries! ${}{}{}{}$
23h
comment What is meant by $AB$ in boolean algebra?
Done :-) ${}{}{}$
1d
comment How does the author apply the implicit function theorem?
How do you define $df(p)$?
1d
comment Eliminating equality constains
You have $A(F z +x_0) = A x_0 = b$ for all $z$ and furthermore, if $Ax=b$ there is some $z$ such that $x=Fz+x_0$.
1d
comment How does the author apply the implicit function theorem?
Wasn't than one of the assumptions? $df(p)$ surjective?
1d
comment Solving eqn. of the form K = AGL + BGT, where A,B,L,T are invertible matrices.
The control theory literature, Riccati equations, Lyapunov equations maybe?