Jurnal
Determine the Determinant of 4xn Non-Square Matrix Using Radić’s Determinant
Unnes Journal of Mathematics · Vol. 13 No. 2 (2025) · hlm. 29–38
- ISSN
- 2460-5859, 2252-6943
- Terbit
- 2025-06-11
- Penerbit
- Universitas Negeri Semarang
- Bahasa
- eng
Abstrak
A non-square matrix is a matrix that has a different number of rows and columns. In the modified double-guard Hill cipher algorithm, a non-square matrix is used as the private key matrix that plays a role in the message encryption and decryption process. Therefore, the determinant of the key matrix is needed to obtain the inverse of the key matrix. Mirko Radić defined the determinant of matrix Amxn, m 4, using Radić’s determinant and an example of its use. The result of this research are the following theorem. If a non-square matrix R = [\matrix (1&0&0&...&0&0@0&1&0&...&0&0@0&a_1&a_2&...&a_i&0@0&0&0&...&0&1)], ai ∈ R, ∀i=1,2,...,n-2 where n>4 then |R|= Σ (-1)i+1 ai, for n odd and Σ (-1)i ai, for n even where i=2 to n-2. The use of the theorem is shown in an example problem using the modified double-guard Hill cipher where matrix R is chosen as the private key matrix. Several conditions must be met by the matrix R to be selected as the key matrix, including all elements of matrix R being positive integers, |R|\neq 0, and R invertible in modulo 128.
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- State University of Semarang
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| Rekan penulis | Organisasi | Artikel bersama |
|---|---|---|
| Emi Pujiastuti | State University of Semarang | 3 |
| Scolastika Mariani | State University of Semarang | 2 |
| Farida Nursyahidah | State University of Semarang | 2 |
| Wardono | State University of Semarang | 1 |
| Wardono Wardono | State University of Semarang | 1 |
| Najmah Fithria Qothrunnada | State University of Semarang | 1 |
| Fenti Nugraheni | State University of Semarang | 1 |
| Zaenuri Mastur | State University of Semarang | 1 |
| Isti Hidayah | State University of Semarang | 1 |
| Ema Khoerunnisa | State University of Semarang | 1 |
| Muhammad Abdul Aziz | State University of Semarang | 1 |
| Rochmad Rochmad | State University of Semarang | 1 |
| Isnarto Isnarto | State University of Semarang | 1 |
| Nila Kumoro Manah | State University of Semarang | 1 |
| P. Widyaningrum | State University of Semarang | 1 |
| Aizzatun Nikmah | State University of Semarang | 1 |
| Endang Retno Winarti | State University of Semarang | 1 |
| Novia Wulan Dary | State University of Semarang | 1 |
| Mashuri Mashuri | State University of Semarang | 1 |
| Siti Aminah Silviani | State University of Semarang | 1 |
| Oktriviani Dewi | State University of Semarang | 1 |
| Safana Aulia Faza | State University of Semarang | 1 |
| Kartono Kartono | State University of Semarang | 1 |
| Rohmatin Zukhriya | State University of Semarang | 1 |
| Sukestiyarno Sukestiyarno | Afiliasi tidak diketahui | 1 |
| Zainnur Wijayanto | State University of Semarang | 1 |
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