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Determinant and Inverse of Matrices of Real Elements

100%

Tamura N., Nakamura Y.

Formalized Mathematics

2007

tom 15

nr 3

127-136

In this paper the classic theory of matrices of real elements (see e.g. [12], [13]) is developed. We prove selected equations that have been proved previously for matrices of field elements. Similarly, we introduce in this special context the determinant of a matrix, the identity and zero matrices, and the inverse matrix. The new concept discussed in the case of matrices of real numbers is the property of matrices as operators acting on finite sequences of real numbers from both sides. The relations of invertibility of matrices and the "onto" property of matrices as operators are discussed.

A Theory of Matrices of Real Elements

81%

Nakamura Y., Tamura N., Chang W.

Formalized Mathematics

2006

tom 14

nr 1

21-28

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.

Ograniczanie wyników

2 Formalized Mathematics

2 Nakamura Y.

2 Tamura N.

1 Chang W.

1 2007

1 2006

Wyniki wyszukiwania

Determinant and Inverse of Matrices of Real Elements

A Theory of Matrices of Real Elements