Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

The Product and the Determinant of Matrices with Entries in a Field


Katarzyna Zawadzka
Warsaw University, Bialystok

Summary.

Concerned with a generalization of concepts introduced in [14], i.e. there are introduced the sum and the product of matrices of any dimension of elements of any field.

MML Identifier: MATRIX_3

The terminology and notation used in this paper have been introduced in the following articles [19] [8] [24] [20] [13] [25] [6] [7] [3] [5] [4] [17] [23] [16] [18] [11] [10] [9] [14] [22] [15] [1] [21] [26] [2] [12]

Contents (PDF format)

  1. Auxiliary Theorems
  2. The Product of Matrices
  3. Determinant

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. Curried and uncurried functions. Journal of Formalized Mathematics, 2, 1990.
[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Basic functions and operations on functions. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Binary operations applied to finite sequences. Journal of Formalized Mathematics, 2, 1990.
[10] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[11] Czeslaw Bylinski. Semigroup operations on finite subsets. Journal of Formalized Mathematics, 2, 1990.
[12] Czeslaw Bylinski. Subcategories and products of categories. Journal of Formalized Mathematics, 2, 1990.
[13] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[14] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.
[15] Katarzyna Jankowska. Transpose matrices and groups of permutations. Journal of Formalized Mathematics, 4, 1992.
[16] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[17] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[18] Andrzej Trybulec. Semilattice operations on finite subsets. Journal of Formalized Mathematics, 1, 1989.
[19] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[20] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[21] Andrzej Trybulec and Czeslaw Bylinski. Some properties of real numbers operations: min, max, square, and square root. Journal of Formalized Mathematics, 1, 1989.
[22] Andrzej Trybulec and Agata Darmochwal. Boolean domains. Journal of Formalized Mathematics, 1, 1989.
[23] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[24] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[25] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[26] Katarzyna Zawadzka. Sum and product of finite sequences of elements of a field. Journal of Formalized Mathematics, 4, 1992.

Received May 17, 1993


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