Segre characteristic

We note that classical information is not distorted since the system operators r depend entirely on T2. However, from the consistency relations, Eqs. (G.6) and (G.7), we have established that T -> 0 as p, but also that Eqs. (G.5) and (G.7) break down at p = proving that IP is a Jordan matrix with Segr characteristic n = 2. Hence, we have proven that there is a singularity at the precise value p =, as well as the following theorem Theorem At the degenerate point p = the truth matrix T is singular, i.e., it is dissimilar to the zero matrix 0 since... 

Summarizing we find that the classical contradiction or paradox related with the Godel proposition G has been represented by a matrix degeneracy with a Segre characteristic equal to two. In this formulation, we have reproduced a truth functional propositional calculus by quantum-like" states determined by probability operators/functions. This allows the case p = to... 

In these extended applications, the possible occurrence of degeneracies, with Segre characteristics larger than one, could result in an unwelcome calculational breakdown - usually considered as a numerical accident brought forward by the self-orthogonality of the transformed vectors. The objective of a successful computation was to stay away from them. 

We will first discuss the simple transformation of a 2 X 2 matrix to complex symmetric form. The model is quite general. We will further establish a simple condition for degeneracy with Segre characteristic r = 2 (see Refs. [6,9,10]). We will consider a specific metric A, which in general may not be positive definite. We will distinguish between two principal cases (1) All 22 12 21 0 and (2) An = — A22 = 1 A12 = A21 = 0. 

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