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A Theory of Matrices of Real Elements

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Nakamura Y., Tamura N., Chang W.
Formalized Mathematics
|
2006
|
tom 14
|
nr 1
21-28
EN
Here, the concept of matrix of real elements is introduced. This is defined as a special case of the general concept of matrix of a field. For such a real matrix, the notions of addition, subtraction, scalar product are defined. For any real finite sequences, two transformations to matrices are introduced. One of the matrices is of width 1, and the other is of length 1. By such transformations, two products of a matrix and a finite sequence are defined. Also the linearity of such product is shown.
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Invertibility of Matrices of Field Elements

100%
Nakamura Y., Oniumi K., Chang W.
Formalized Mathematics
|
2008
|
tom 16
|
nr 2
195-202
EN
In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of field elements are also introduced as a preparation.MML identifier: MATRIX14, version: 7.9.01 4.101.1015
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