A special linear associative algebra

Discriminant Matrices of a Linear Associative Algebra

where ti(eres) and fa{erea) are the first and second traces, respectively, of eres. The first forms in terms of the constants of multiplication arise from the isomorphism between the first and second matrices of the elements of A and the elements themselves. The second forms result from direct calculation of the traces of R(er)R(es) and S(er)S(es), R{ei) and S(ei) denoting, respectively, the fi...

Special Relativity and Linear Algebra

Before Einstein’s publication in 1905 of his theory of special relativity, the mathematical manipulations that were a product of his theory were in fact already known. The so called Lorentz transformations were tricks that had been found that allowed the speed of light to propagate in all directions at the same speed, which accounted for its strange behavior when traveling through the now infam...

Making Non - Associative Algebra Associative Pei

Based on results about open string correlation functions, a nonassociative algebra was proposed in a recent paper for D-branes in a background with nonvanishing H. We show that our associative algebra obtained by quantizing the endpoints of an open string in an earlier work can also be used to reproduce the same correlation functions. The novelty of this algebra is that functions on the D-brane...

Linear Algebra . A publication of the International Linear Algebra Society

Nonnegative nilpotent lower triangular completions of a nonnegative nilpotent matrix are studied. It is shown that for every natural number between the index of the matrix and its order, there exists a completion that has this number as its index. A similar result is obtained for the rank. However, unlike the case of complex completions of complex matrices, it is proved that for every nonincrea...

ON GENERALIZED INVERSES IN A LINEAR AsSOCIATIVE ALGEBRA AND THEIR APPLICATIONS