Krasimir Yordzhev

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 4, Pages 133—143

DOI: 10.7546/nntdm.2018.24.4.133-143

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## Details

### Authors and affiliations

Krasimir Yordzhev

*Faculty of Mathematics and Natural Sciences
South-West University “Neofit Rilski”
Blagoevgrad, Bulgaria*

### Abstract

The work considers an equivalence relation in the set of all *n* × *m* matrices with entries in the set [*p*] = {0, 1, … *p* − 1}. In each element of the factor-set generated by this relation, we define the concept of canonical matrix, namely the minimal element with respect to the lexicographic order. We have found a necessary and sufficient condition for an arbitrary matrix with entries in the set [*p*] to be canonical. For this purpose, the matrices are uniquely represented by ordered *n*-tuples of integers.

### Keywords

- Permutation matrix
- Weighing matrix
- Hadamard matrix
- Semi-canonical matrix
- Canonical matrix
- Ordered
*n*-tuples of integers

### 2010 Mathematics Subject Classification

- 05B20
- 15B36

### References

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## Cite this paper

Yordzhev, K. (2018). Canonical matrices with entries integers modulo *p*. *Notes on Number Theory and Discrete Mathematics*, 24(4), 133-143, doi: 10.7546/nntdm.2018.24.4.133-143.