Proceedings of the 2004 workshop on directions in combinatorial matrix theory, Banff, Canada, May 7--8, 2004.
Proceedings of the 2004 workshop on nonnegative matrices, Maynooth, Ireland, July 11--14, 2004.
Product of exponentials and spectral radius of random k-circulants
We consider n × n random k-circulant matrices with n → ∞ and k = k(n) whose input sequence {al}l≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + δ) moment. We study the asymptotic distribution of the spectral radius, when n = kg + 1. For this, we first derive the tail behaviour of the g fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we show that with appropriate scaling...
Product of operators and numerical range preserving maps
Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of by . This includes the usual product and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying such that ϕ: V → V has the form A...
Product of range symmetric block matrices in Minkowski space.
Products of commuting nilpotent operators.
Products of idempotent matrices over Hermite domains.
Products of Infinite-Dimensional Non-Negative Matrices; Extension of Hajnal's Results.
Products of -matrices and nested sequences of principal minors.
Products of simple isometries of given conjugacy types.
Products of stochastic matrices and applications.
Produit tensoriel de matrices, homologie cyclique, homologie des algèbres de Lie
On munit, naturellement, d’un surproduit l’algèbre extérieure de l’homologie cyclique d’une -algèbre commutative ( étant un corps de caractéristique zéro) à l’aide du produit de Loday-Quillen. On munit d’un surproduit l’homologie de l’algèbre de Lie du groupe linéaire général de à l’aide du produit tensoriel de matrices. On montre que l’isomorphisme d’algèbres de Hopf de Loday-Quillen est compatible avec les surproduits définis ci-dessus. On obtient ainsi une interprétation du produit de Loday-Quillen,...
Produit tensoriel topologique de corps valués
Produit tensoriel topologique des corps values.
Professor Haruo Yanai and multivariate analysis
The late Professor Yanai has contributed to many fields ranging from aptitude diagnostics, epidemiology, and nursing to psychometrics and statistics. This paper reviews some of his accomplishments in multivariate analysis through his collaborative work with the present author, along with some untold episodes for the inception of key ideas underlying the work. The various topics covered include constrained principal component analysis, extensions of Khatri’s lemma, theWedderburn-Guttman theorem,...
Projections of tensor spaces
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten.
Proof of the alternating sign matrix conjecture.
Proof of the combinatorial nullstellensatz over integral domains, in the spirit of Kouba.
Properties of a covariance matrix with an application to -optimal design.