There are various statements in the physics literature about stratification of quantum states, for example into orbits a unitary group, and generalized differentiable structures on it. Our aim is to clarify make precise some these statements. For A an arbitrary finite-dimensional C*-algebra U(A) group elements A, we observe that partition state space S(A) not decomposition orbit types (its piec...

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.

The main result of this short note is a generic version of Paz’ conjecture on the length of generating sets in matrix algebras. Consider a generic g-tuple A = (A1, . . . , Ag) of n × n matrices over an infinite field. We show that whenever g ≥ n, the set of all words of degree 2d in A spans the full n × n matrix algebra. Our proofs use generic matrices, are combinatorial and depend on the const...

Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units [Formula: see text] etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Bu...

We present new, e cient algorithms for some fundamental computations with nite dimensional (but not necessarily commutative) associative algebras over nite elds. For a semisimple algebra A we show how to compute a complete Wedderburn decomposition of A as a direct sum of simple algebras, an isomorphism between each simple component and a full matrix algebra, and a basis for the centre of A. If ...

Description Extended Structural Equation Modelling (SEM). Models may be specified with reticular action model (RAM) matrices or paths,linear structural relations (LISREL) matrices or paths, or directly in matrix algebra. To increase modularity, model expectations,fit functions, and optimizers can be easily interchanged. Fit functions include full information maximum likelihood (FIML),maximum li...

For each 1 < s < ∞, a Popa algebra As is constructed that embeds as a weakly dense C∗–subalgebra of the interpolated free group factor L(Fs). Certain approximation properties for As are shown. It follows that L(Fs) has the weak expectation property of Lance with respect to As. In the course of the demonstration, it is proved that under certain conditions, full amalgamated free products of matri...