| Autor: |
Wannisa Apairat, Sompong Chuysurichay |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
Songklanakarin Journal of Science and Technology (SJST), Vol 45, Iss 2, Pp 308-313 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
0125-3395 |
| Popis: |
For any positive integer 𝑛 ≥ 2, we give necessary and sufficient conditions of the existence of the Moore-Penrose inverse of any square matrix over the ring of integers modulo 𝑛. In particular, the formula for the Moore-Penrose inverse of any 2 × 2 matrix is also explained if it exists. We also characterize all values of 𝑘 and 𝑛 for which the ring of all 𝑘 × 𝑘 matrices over the ring of integers modulo 𝑛 is ∗-regular with respect to the matrix transposition as an involution. It turns out that the ring of 𝑘 × 𝑘 matrices over the ring of integers modulo 𝑛 is ∗-regular if and only if 𝑛 is square-free and either 𝑘 = 1 or 𝑘 = 2 and each prime divisor of 𝑛 must have the form 4𝑚 + 3 for some nonnegative integer 𝑚. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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