# Definition and some Properties of Information Entropy

Formalized Mathematics (2007)

• Volume: 15, Issue: 3, page 111-119
• ISSN: 1426-2630

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## Abstract

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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 to index. Then we define each concept of information entropy for a probability sequence and two kinds of probability matrices, joint and conditional, that are defined in article [25]. Further, we discuss some properties of information entropy including Shannon's lemma, maximum property, additivity and super-additivity properties.

## How to cite

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Bo Zhang, and Yatsuka Nakamura. "Definition and some Properties of Information Entropy." Formalized Mathematics 15.3 (2007): 111-119. <http://eudml.org/doc/267443>.

@article{BoZhang2007,
abstract = {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 to index. Then we define each concept of information entropy for a probability sequence and two kinds of probability matrices, joint and conditional, that are defined in article [25]. Further, we discuss some properties of information entropy including Shannon's lemma, maximum property, additivity and super-additivity properties.},
author = {Bo Zhang, Yatsuka Nakamura},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {111-119},
title = {Definition and some Properties of Information Entropy},
url = {http://eudml.org/doc/267443},
volume = {15},
year = {2007},
}

TY - JOUR
AU - Bo Zhang
AU - Yatsuka Nakamura
TI - Definition and some Properties of Information Entropy
JO - Formalized Mathematics
PY - 2007
VL - 15
IS - 3
SP - 111
EP - 119
AB - 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 to index. Then we define each concept of information entropy for a probability sequence and two kinds of probability matrices, joint and conditional, that are defined in article [25]. Further, we discuss some properties of information entropy including Shannon's lemma, maximum property, additivity and super-additivity properties.
LA - eng
UR - http://eudml.org/doc/267443
ER -

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