Journal of Formalized Mathematics
Volume 7, 1995
University of Bialystok
Copyright (c) 1995 Association of Mizar Users

Associated Matrix of Linear Map


Robert Milewski
Warsaw University, Bialystok

MML Identifier: MATRLIN

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

Contents (PDF format)

  1. Preliminaries
  2. More on Finite Sequence
  3. Matrices and Finite Sequences in Vector Space
  4. Decomposition of a Vector in Basis
  5. Associated Matrix of Linear Map

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Binary operations applied to finite sequences. Journal of Formalized Mathematics, 2, 1990.
[9] Czeslaw Bylinski. Finite sequences and tuples of elements of a non-empty sets. Journal of Formalized Mathematics, 2, 1990.
[10] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[11] Katarzyna Jankowska. Matrices. Abelian group of matrices. Journal of Formalized Mathematics, 3, 1991.
[12] Katarzyna Jankowska. Transpose matrices and groups of permutations. Journal of Formalized Mathematics, 4, 1992.
[13] Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski. Abelian groups, fields and vector spaces. Journal of Formalized Mathematics, 1, 1989.
[14] Michal Muzalewski. Rings and modules --- part II. Journal of Formalized Mathematics, 3, 1991.
[15] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[16] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[17] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[18] Wojciech A. Trybulec. Basis of vector space. Journal of Formalized Mathematics, 2, 1990.
[19] Wojciech A. Trybulec. Linear combinations in vector space. Journal of Formalized Mathematics, 2, 1990.
[20] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Journal of Formalized Mathematics, 2, 1990.
[21] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[22] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Journal of Formalized Mathematics, 2, 1990.
[23] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[24] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[25] Katarzyna Zawadzka. Sum and product of finite sequences of elements of a field. Journal of Formalized Mathematics, 4, 1992.
[26] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Journal of Formalized Mathematics, 5, 1993.

Received June 30, 1995

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