# Definition and some Properties of Information Entropy

Formalized Mathematics (2007)

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

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topBo 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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