Absolute values on algebras H(D)

On Finite-Dimensional Absolute Valued Algebras

This is a study of morphisms in the category of finite dimensional absolute valued algebras, whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two...

Absolute Valued Algebras.

An algebra A over the real field R is a vector space over R which is closed with respect to a product xy which is linear in both x and y, and which satisfies the condition X(xy) = ÇKx)y = x(ky) for any X in R and x, y in A. The product is not necessarily associative. An element e of the algebra A is called a unit element if ex=xe = x for any x in A. Given any subset B of A, dim B will denote th...

Asymptotic Hölder Absolute Values

Weak log-majorization inequalities of singular values between normal matrices and their absolute values

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

Symmetric Polynomials and HD-Quantum Vertex Algebras

In this paper we use a bicharacter construction to define an HDquantum vertex algebra structure corresponding to the quantum vertex operators describing classes of symmetric polynomials.