Basis of Real Linear Space

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

Basis of Real Linear Space

Wojciech A. Trybulec: Warsaw University

Summary.

Notions of linear independence and dependence of set of vectors, the subspace generated by a set of vectors and basis of real linear space are introduced. Some theorems concerning those notions are proved.

MML Identifier: RLVECT_3

The terminology and notation used in this paper have been introduced in the following articles [8] [6] [16] [10] [3] [17] [2] [4] [5] [14] [9] [7] [13] [12] [11] [15] [1]

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Grzegorz Bancerek. The ordinal 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. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[7] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.

[8] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[9] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.

[10] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[11] Wojciech A. Trybulec. Operations on subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.

[12] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.

[13] Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Journal of Formalized Mathematics, 1, 1989.

[14] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.

[15] Wojciech A. Trybulec. Linear combinations in real linear space. Journal of Formalized Mathematics, 2, 1990.

[16] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[17] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received July 10, 1990

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