Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
See all formats and pricing
More options …
Volume 14, Issue 3 (Jan 2006)

Issues

The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements

Bo Zhang
  • Shinshu University, Nagano, Japan
/ Yatsuka Nakamura
  • Shinshu University, Nagano, Japan
Published Online: 2008-06-09 | DOI: https://doi.org/10.2478/v10037-006-0012-1

The Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elements

In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.

  • [1] Kanchun and Yatsuka Nakamura. The inner product of finite sequences and of points of n-dimensional topological space. Formalized Mathematics, 11(2):179-183, 2003.Google Scholar

  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Google Scholar

  • [4] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Google Scholar

  • [5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Google Scholar

  • [6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

  • [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [8] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Google Scholar

  • [9] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.Google Scholar

  • [10] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.Google Scholar

  • [11] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.Google Scholar

  • [12] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Google Scholar

  • [13] Jarosław Kotowicz and Yatsuka Nakamura. Introduction to Go-board - part I. Formalized Mathematics, 3(1):107-115, 1992.Google Scholar

  • [14] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.Google Scholar

  • [15] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Google Scholar

  • [16] Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.Google Scholar

  • [17] Yatsuka Nakamura, Nobuyuki Tamura, and Wenpai Chang. A theory of matrices of real elements. Formalized Mathematics, 14(1):21-28, 2006.Google Scholar

  • [18] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.Google Scholar

  • [19] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.Google Scholar

  • [20] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.Google Scholar

  • [21] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.Google Scholar

  • [22] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Google Scholar

  • [23] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [24] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Google Scholar

  • [25] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.Google Scholar

About the article


Published Online: 2008-06-09

Published in Print: 2006-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-006-0012-1.

Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in