Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

Linear Combinations in Vector Space

Wojciech A. Trybulec
Warsaw University
Supported by RPBP.III-24.C1.

Summary.

The notion of linear combination of vectors is introduced as a function from the carrier of a vector space to the carrier of the field. Definition of linear combination of set of vectors is also presented. We define addition and subtraction of combinations and multiplication of combination by element of the field. Sum of finite set of vectors and sum of linear combination is defined. We prove theorems that belong rather to [6].

MML Identifier: VECTSP_6

The terminology and notation used in this paper have been introduced in the following articles [7] [12] [5] [2] [13] [3] [4] [8] [1] [9] [6] [10] [11]

Contents (PDF format)

Bibliography

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[7] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[8] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.
[9] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[10] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[11] Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Journal of Formalized Mathematics, 2, 1990.
[12] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[13] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received July 27, 1990