Terry Loring
  • Member for 11 years, 8 months
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Which journals publish expository work?
36 votes

From their website: "Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles." A search in Math ...

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Universal $C^*$-algebra with generators and relations
18 votes

Since free C*-algebras don't exist, we can't give a concrete description of all relations that are allowed. Instead, we need to give axioms that determine what collections of n-tuples $(a_1,\dots,a_n)...

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Any real contribution of functional analysis to quantum theory as a branch of physics?
17 votes

As jjcale mentions in a comment, the index of a Fredholm operator is very important in physics. One way to define the Chern number of a topological insulator is in terms of the index of a Fredholm ...

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Applications of the "almost commuting" theorem of H. Lin
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15 votes

Lin's theorem shows the existence of a localized basis for the low-energy space in models of non-interacting fermions on a finite lattice on a disk. This was observed by Matt Hastings. See "Topology ...

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Free C^*-algebra
11 votes

See Lemma 3.7 in my paper C*-relations, Math. Scand., 107(1), 43--72 (2010). I show that this seminorm is actually a norm. This is for the finite or infinite case. For the case of countably many ...

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Reference request for translating from Top to C*-alg
10 votes

Gert Pedersen wrote "In a careless moment a C*-algebraist might be quoted for saying that there is a covariant functor between the categories of commutative C*-algebras with morphisms and the category ...

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Nearby matrices have nearby leading eigenvectors?
7 votes

You can get a nice estimate using the spectral norm. Theorem 3.2.32 of Bratteli and Robinson vol. 1 tell us an estimate on $f(A) - f(B)$ for a variety of functions. Take $f:\mathbb R \rightarrow \...

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The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics
6 votes

The Chern numbers, Spin Chern numbers and so forth in condensed matter physics are very important in understanding topological insulators. There are many ways to compute this invariants, and some of ...

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Polar decomposition for quaternionic matrices?
6 votes

For all matrices, even non-invertible matrices, one gets a polar decomposition $X=UP$ with $U$ unitary and $P$ positive semidefinite. Of course $U$ is not unique unless $X$ is invertible. I ...

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K-theory for the $C^*-$algebra of the continuous functions on the $2-$torus and the Bott projection
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5 votes

If you want an explicit projection, you can form a variation of a Rieffel projection as follows. First take any function $f$ from $[-\pi/2,\pi/2]$ to $[0,1]$ that sends $-\pi/2$ to $1$, dips down to $...

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Who first identified the universal $C^*$-algebra generated by an idempotent of norm at most $C$?
5 votes

I almost found it: Example 4.4 in "Presentations and Tietze transformations of C*-algebras" by Will Grilliette, New York J. Math. 18 (2012) 121--137. The generator in the concrete algebra is not ...

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Numerical method for simultaneous computation of eigenvalues of a family of commuting matrices
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4 votes

For small Hermitian (or real symmetric) matrices, yes, but really this is a hard problem not fully solved. See [1,2] for algorithms. The Cardoso paper [2] looks at the non-commuting case, but in the ...

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Classification of finite-dimensional real super C*-algebras
3 votes

I was looking for this a few years ago, and found it in the appendix of this paper. El-kaïoum, M. Moutuou. "Graded Brauer groups of a groupoid with involution." Journal of Functional Analysis 266.5 (...

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explicit description of the product map in K-theory
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3 votes

I believe the correct formula is $$(u-1_{A^+}) \otimes p + 1_{(A \otimes B)^+}$$ which makes sense if you work this out in the following special case. Let $A$ be $C_0(0,1)$ and let $B$ be $C(\{0,1\})...

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Computing signature
3 votes

This seems to be an $O(n^3)$ problem, so if your matrix is smaller than 100 by 100 you might as well use an eigensolver. For bigger matrices you can use Newton's method (see Higham's papers or book)...

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How to calculate $(A^{-1})_{ii}$ for an invertible hyperhermitian quaternionic matrix $A$?
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3 votes

Determinants are tricky for matrices of quaternions, but they are not as bad when the matrix is hermitian. In that case, one can expand in the usual way along any row and get the same result. See ...

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Diagonalization of quaternion matrices
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3 votes

I am rather certain that you cannot modify a standard diagonalization to the structured diagonalization that you want. I have seen such a method used, but it is expected to fail occasionally, ...

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Sample from a delta-ball in the orthogonal group O(n)
3 votes

I have not proven the following to work, but I've done similar calculations when debugging software in my 2009-10 work with Matt Hastings. If these seem fast enough, it should not be too much work to ...

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Pullbacks of $C^*$-algebras
2 votes

Both $\mathrm{id}$ and $\sigma\circ\chi$ map from $A \oplus_C B$ to $A \oplus_C B$ respecting the left and right projection maps. (I leave to the reader the writing out of the diagrams.) Since $A ...

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Exponential of large matrices
2 votes

Have a look at a recent paper discussing how matrix sparseness and locality go together: "Decay Properties of Spectral Projectors with Applications to Electronic Structure" by Benzi et al. in SIAM ...

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On certain decomposition of unitary symmetric matrices
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2 votes

Here is a way to answer the second question. I am assuming complex matrices and using '$X^{*}=\overline{X}^{\mathrm{T}}$. The first question (already answered by Suvrit ) I discuss at the end. ...

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Approximate eigenvectors for a set of non-commuting self-adjoint operators
1 votes

I can give you a few papers, and these have references to others. I discuss joint approximate eigenvectors in the context of approximate joint measurement in [1]. You need to know that often it is $...

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