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Definition and some Properties of Information Entropy

Bo ZhangYatsuka Nakamura — 2007

Formalized Mathematics

In this article we mainly define the information entropy [3], [11] and prove some its basic properties. First, we discuss some properties on four kinds of transformation functions between vector and matrix. The transformation functions are LineVec2Mx, ColVec2Mx, Vec2DiagMx and Mx2FinS. Mx2FinS is a horizontal concatenation operator for a given matrix, treating rows of the given matrix as finite sequences, yielding a new finite sequence by horizontally joining each row of the given matrix in order...

Pseudo-Riemannian weakly symmetric manifolds of low dimension

Bo ZhangZhiqi ChenShaoqiang Deng — 2019

Czechoslovak Mathematical Journal

We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions 2 and 3 , based on the algebraic approach of such spaces through the notion of a pseudo-Riemannian weakly symmetric Lie algebra. We also study the general symmetry of reductive 3 -dimensional pseudo-Riemannian weakly symmetric spaces and particularly prove that a 3 -dimensional reductive 2 -fold symmetric pseudo-Riemannian manifold must be globally symmetric.

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