Related papers: On Hadamard matrices at roots of unity
This manuscript has been withdrawn by the author. Some of the material has been included in the manuscript 'Dualizing the Dual Standard Model' hep-ph/0102084.
This paper has been withdrawn by the author.
This paper has been withdrawn by the author.
This paper has been withdrawn by the authors, due to a mistake pointed out by Lenny Ng and Josh Sabloff.
This paper has been withdrawn by the authors, due to the discovery of paper 0201028 which predates it and contains most of it's results.
This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2
This paper has been withdrawn by the author and the content is merged into a new paper: H-Theorem and Generalized Entropy Composition with Different q Indices: cond-mat/9912454.
This paper has been withdrawn by the authors due to a more research needed to estimate $h^{*}_{n}(b)$ which really should be written as $h^{*}_{n}(b,A)$ for $b\in \Gamma (t)$.
This paper has been withdrawn by the authors, because of a crucial gap in the proof of the main theorem.
This paper has been withdrawn by the authors as requested by the journal.
This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is…
This paper has been withdrawn by the author since the proof of Lemma 8 is not correct.
We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…
We study $m \times n$ matrices whose columns are of the form \[\{(a_{1j},\ldots, a_{nj}): \quad a_{1j} = \lambda_j,\ a_{ij} = \pm\lambda_j\ , \ \lambda_j >0 ,\ j=1,2,\ldots,n\}.\] We explicitly construct for all $a = (a_1,\ldots,…
This paper has been withdrawn.
This paper has been withdrawn by the author due to incomplete interpretation for the results.
This paper has been withdrawn by the author and it is published in AGAG
This paper has been withdrawn due to an error, and no further revisions will be made.
This paper has been withdrawn by the authors in order to replace it with a more correct treatment. The basic results remain the same but the treatment is more rigorously correct.
This paper was withdrawn by the authors.