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seen Oct 9 '12 at 3:52

Oct
6
comment Bessel functions with complex coefficients
Mathematica of course has what yo want ... but you probably do not want it. I understand that Bessel Function is a function of exponential decay...so I am wondering if computing the Taylor series to few hundred terms (with Stirling approximation for the Gamma function) is not an option ?
Oct
6
comment Are there any decompositions of a symmetric matrix that allow for the inversion of any submatrix?
Assuming your matrix is real matrix (all elements are real), you are guaranteed by spectral theorem that your matrix $A = QDQ^{T}$ where $D$ is diagonal and $Q$ is orthogonal. Getting this $Q$ is algorithmically Gram-Schimdt process (so rather simple).
Sep
21
comment A basic question on relative singular groups\homology
Example $H_{1} \subset G_{1}$ and $H_{2} \subset G_{2}$ are two groups and their subgroups and $\phi : G_{1} \rightarrow G_{2}$ is any homomorphism taking $H_{1}$ into $H_{2}$ then we get a well defined homomorphism (assuming$H_{1}$ and $H_{2}$ are both normal; which is true in abelian case) of the groups $G_{1}/H_{1} \rightarrow G_{2}/H_{2}$.
Sep
21
comment A basic question on relative singular groups\homology
Yes you are right the boundary map descends to the quotient nicely for any subspace $A$ but the associated homology theory will not be nice unless some extra conditions on $A$ are fulfilled.
Sep
20
comment Methods of Multilinear Algebra in Representation Theory
The study of Lie algebras over $\mathbb{C}$ becomes easy once you have understood $\mathfrak{sl}_{2}$ and it might be a great idea to work out symmetric and tensor products of representation in this case by hand. Fulton Harris does that and if I remember correctly they have a beautiful (and very verbose) discussion on that topic.
Sep
20
comment Methods of Multilinear Algebra in Representation Theory
Thanks! for the link
Sep
18
comment Segre embedding
This map is a closed embedding into $\mathbb{P}^{rs+r+s}$ which means that the image is a closed algebraic subscheme (or rather subvariety). To show this show that in any affine patch of $\mathbb{P}^{rs+r+s}$ the points of the Segre embedding correspond to an ideal. Writing co-ordinates for $\mathbb{P}^{rs+r+s}$ as $k[X_{ij}]$ where $0\leq i\leq r$ and $0 \leq j \leq s$ we see that the image of the Segre embedding correspond to the ideal generated by all $2 \times 2$ minors of the matrix $(X_{ij})$. This shows that the image is closed.
Sep
17
comment Is it possible to practice mental math too often?
You might be hitting the so called "ok plateau".
Sep
16
comment Proving something by copying down axioms and changing variable names?
You need to assert that an axiom is true in your case of this set of even functions. Then check that your assertion is true.
Sep
16
comment (Symmetric) group acting on a graph
Here is an attempt: Let $f: X \rightarrow Y$ be a surjective map of graphs (vertices surject onto vertices and so do edges; basically it is a contraction of certain edges and vertices)then we can talk about the group Aut(X/Y) which are graph automorphisms of $X$ commuting with the map $f$. In your case group $P$ is the group $Aut(\tilde{X}/(X/G))$. Well here $\tilde{X}=$ universal cover of $X$ and $X/G$ the quotient graph of $X$ by $G$.
Sep
15
comment homeomorphism question relating to the topological 3-sphere
@MarianoSuárez-Alvarez, I recall when I was first learning this stuff, this question stumped me for some time. Where as when you look at any sphere (after learning some basic general topology) the idea of breaking it up into two hem-spheres seems much more natural.
Sep
15
comment Is the set of integer coefficient polynomials countable?
@Thomas Andrews, Yes I meant the polynomial algebra not a single polynomial per se.
Sep
14
comment Is the set of integer coefficient polynomials countable?
An integral polynomial gives a function from $\mathbb{Z} \rightarrow \mathbb{Z}$. A power series doesn't. A polynomial is a finitely generated algebra over the co-efficient ring a power series is not.
Sep
14
comment Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$?
A hlibert space is still a vector space...what do you mean by a operator which is not linear?
Sep
14
comment homeomorphism question relating to the topological 3-sphere
You are talking about the usual construction of $S^{3}$ the one asked is bit unusual. In general there are many ways to triangulate a surface (and here break up a solid into polyherdral parts: essentially a CW complex). If you keep track of the smaller parts and their intersections you can decompose the solid into more manageable parts. The question is showing the sphere is two solid tori.
Sep
13
comment The matrix exponential: Any good books?
For finite dimensional matrices you are essentially talking about exponential maps on lie groups. So look up any elementary nook on lie algebras and lie groups (may be it is worthwhile to consider compact lie groups first). Off hand I can think of M.Artin's Algebra, Bump's Lie Groups.
Sep
13
comment Notation Issues
I am guessing here, but most likely $S^{\star}X$ would be the space of Schwartz Bruhat functions on $X$. If you do not know what that is it is better to work with a healthier substitute and you can assume $S^{\star}X$ is space of smooth (infinitely differentiable) compactly supported real functions on $X$.
Sep
13
comment What branch of mathematics is most needed in the industry or how one can make living with mathematics (apart from teaching)?
I think you need to define relevant job more clearly. If you wish to maximize your chances at a financial institution studying economics or perhaps mathematical economics is more useful. Studying mathematics for that purpose is not the most efficient route.
Sep
13
comment Proving that there are infinitely many primes with remainder of 2 when divided by 3
Use Dirichlet's theorem on primes in Arithmetic progressions. Well it is an overkill but you don't have to do anything.en.wikipedia.org/wiki/Primes_in_arithmetic_progression
Sep
13
comment I've heard that some kinds of mathematics are so abstract, what's the point in it?
I do not understand if you mean abstraction of programing languages in a concrete technical sense or a rather loose figurative sense. But, mathematics is no more abstract to a mathematician than playing a (difficult) piece of music to a pianist. Of course to an outside r it looks strange and esoteric.