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location Albany, CA
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visits member for 2 years, 7 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.


13h
comment z and w are two complex numbers prove the relationship
There is some awkwardness with $\operatorname{arg}$ which I am avoiding, computations should be performed modulo $2 \pi$. For example, depending on how you compute $\operatorname{arg}$, if you take $z=1, w=-i$, then $\operatorname{arg}z = 0, \operatorname{arg}w = {3 \over 2} \pi$ from which we get $\operatorname{arg}z - \operatorname{arg}w = - {3 \over 2} \pi$. Of course, modulo $2 \pi$ this gives the desired result.
13h
comment z and w are two complex numbers prove the relationship
If $\operatorname{re} v = 0$, then $v$ is purely imaginary, hence $v = |v| e^{i \theta}$, where $\theta = \pm { \pi \over 2}$.
13h
comment A basic doubt to compute exponential of a matrix
@WillJagy: Funny! (Btw, I think the gerbils might find a Schur form to be preferable to the Jordan normal form from a numerical standpoint...)
13h
comment z and w are two complex numbers prove the relationship
This is just the analytic version of Daniel's parallelogram approach.
13h
comment z and w are two complex numbers prove the relationship
If the number is imaginary?
13h
comment Taylor polynomial converging pointwise but not uniformly?
Also, $f(x) = e^x$ doesn't converge uniformly on $\mathbb{R}$. As Andres points out, on compact sets the convergence (within the ROC) is uniform, so any example must be on a non-compact set.
14h
comment Taylor polynomial converging pointwise but not uniformly?
Try the Taylor series for $f(x) = {1 \over 1-x}$ on $(-1,1)$.
14h
comment How to calculate anti log for this special case?
If $x = \log_b y$, then $y = b^x$. You need to know the base of the logarithm.
14h
comment A basic doubt to compute exponential of a matrix
@ChristianBlatter: It was a joke. The original paper was titled something like "19 dubious ways to compute the exponential". I used to work with the old (free) Fortran version of Matlab which even had the rtfm command.
14h
comment Real Analysis Cardinality Proof
@TomCollinge: I understand, this was a hint...
23h
comment Can the zero vector be an eigenvector for a matrix?
The eigenpolice are coming...
1d
comment Prove True or false : If $A$ and $B$ are $n\times n$ invertible matrices, then the rows of $A$ form a basis for $\mathbb{R}^n$
What's $B$ got to do with it (with appropriate music in background)?
1d
comment The expected value of a random vector when the X_is are independent
I liked this presentation: et.bs.ehu.es/~etptupaf/nuevo/ficheros/stat4econ/muestreo.pdf.
1d
comment A basic doubt to compute exponential of a matrix
@WillJagy: That's a little dubious :-).
1d
comment integral over limsup of numerical function
It is not true, this is a counterexample.
1d
comment Prove that theorems about trace of matrix:
The minimal polynomial is the minimum degree monic polynomial $\psi_A$ such that $\psi_A(A) = 0$. It is easy to show that if $p$ is a polynomial such that $p(A) = 0$, then $\psi_A \mid p$. Also, if $Av=\lambda v$, then $\psi_A(A)v = 0 = \psi_A(\lambda)v$ and so any eigenvalue is a zero of $\psi_A$. In the above example, we see that we must have $\psi_A(x) = x^l$ for some $l$, hence all the eigenvalues are zero.
1d
comment How do I calculate the Trigonometric Fourier Series Coefficients of the following function?
Why not just compute the integrals? Also, the Fourier series of the sum is the sum of the Fourier series, so you can compute them separately and add.
1d
comment Prove that theorems about trace of matrix:
For any matrix $A$ with eigenvalues $\lambda_k$, you have $\operatorname{tr} A = \sum_k \lambda_k$ (see the Jordan form for example). If $A$ has eigenvalues $\lambda_k$ then $A^{-1}$ has eigenvalues ${1 \over \lambda_k}$. If $A^k = 0$ for some $k$, then the minimal polynomial only has roots at zero, hence all eigenvalues are zero.
1d
comment Does there exists a vector v such that $Av\neq 0$ but $A^{2}v=0$
Sorry, I really don't understand what you are saying/asking.
1d
comment Does there exists a vector v such that $Av\neq 0$ but $A^{2}v=0$
I don't understand what you are asking. The choice is not arbitrary, it is chosen so that $Av \neq 0$ and $A^2v=0$. However, it is not unique, we could have chosen $v=e_1+e_2$ for example.