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http://repository.ipb.ac.id/handle/123456789/112907
Title: | Determinan dan Invers Matriks Skew Circulant dengan Entri Bilangan Pell-Lucas |
Authors: | Mas'oed, Teduh Wulandari Guritman, Sugi Auliasari, Devi |
Issue Date: | 2022 |
Publisher: | IPB University |
Abstract: | Matriks skew circulant adalah matriks persegi yang entrinya bergeser satu
kolom secara berurutan ke kanan dan semua entri yang berada di bawah diagonal
utama akan bernilai negatif, sehingga untuk mengetahui seluruh entri matriks
skew circulant dapat dilihat dari salah satu baris dari matriks tersebut. Entri-entri
pada matriks skew circulant dapat menggunakan entri dengan berbagai barisan
bilangan, salah satunya adalah bilangan Pell-Lucas. Pada karya ilmiah ini
diformulasikan determinan dan invers matriks skew circulant dengan entri
bilangan Pell-Lucas. Pembuktian formulasi determinan matriks skew circulant
dengan entri bilangan Pell-Lucas diperoleh dari penerapan serangkaian operasi
baris dasar sehingga diperoleh matriks segitiga atas. Sedangkan, formulasi
inversnya diperoleh dengan membuat matriks-matriks representasi dari hasil
serangkaian operasi baris dasar dan operasi kolom dasar. Skew circulant matrix is a square matrix whose entries are shifted one column sequentially to the right and all entries below the main diagonal will be negative, so to find out all the entries of the skew circulant matrix can be seen from any row of the matrix. The entries in the skew circulant matrix can be filled in various sequences of numbers such as Pell-Lucas numbers. In this research, the determinant and inverse of the skew circulant matrix with Pell-Lucas numbers entries are formulated. The proof of the determinant formulation of the skew circulant matrix with Pell-Lucas numbers entries is explained by applying a series of elementary row operations to get the upper triangular matrix. While the proof of the inverse formulation is explained by constructing representational matrices of the results of the series of elementary row operations and elementary column operations. |
URI: | http://repository.ipb.ac.id/handle/123456789/112907 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
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Cover.pdf Restricted Access | Cover | 997.48 kB | Adobe PDF | View/Open |
Fullteks.pdf Restricted Access | Fullteks | 1.16 MB | Adobe PDF | View/Open |
Lampiran.pdf Restricted Access | Lampiran | 486.52 kB | Adobe PDF | View/Open |
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