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Title: | Determinan dan Invers Matriks Skew Left Circulant dengan Entri Bilangan Fibonacci |
Authors: | Mas'oed, Teduh Wulandari Siswandi Mamella, Dwiva |
Issue Date: | 2023 |
Publisher: | IPB University |
Abstract: | Matriks skew left circulant adalah suatu matriks persegi dengan entri baris
bergeser satu kolom secara berurutan ke kiri dan semua entri yang berada dibawah
diagonal sekunder akan bernilai negatif, sehingga untuk mengetahui seluruh
matriks skew left circulant dapat dilihat dari salah satu baris dari matriks tersebut.
Entri-entri dari skew left circulant dapat menggunakan entri dengan berbagai
barisan bilangan, salah satunya adalah dengan barisan bilangan Fibonacci. Pada
karya ilmiah ini diformulasikan determinan dan invers matriks skew left circulant
dengan entri bilangan Fibonacci. Pembuktian Formulasi determinan matriks skew
left circulant diperoleh dari penerapan serangkaian operasi baris dasar pada
matriks skew circulant sehingga diperoleh matriks segitiga atas, dilanjutkan
mengalikan dengan determinan matriks Gamma. Sedangkan, formulasi inversnya
diperoleh dengan membuat matriks-matriks dari matriks skew circulant
representasi dari hasil serangkaian operasi baris dasar dan operasi kolom dasar,
dilanjutkan dengan mengalikan dengan invers matriks Gamma. The left circulant skew matrix is a square matrix with row entries shifted one column sequentially to the left and all entries under the secondary diagonal will be negative, so to find out the entire circulant skew left matrix can be seen just from the first row of the matrix. Entries from the skew left circulant can be filled in various number sequences, one of which is the Fibonacci number sequence. In this scientific work, the determinants and inverses of the skew left circulant matrix are formulated with Fibonacci number entries. Proof The formulation of the skew left circulant matrix determinant is obtained from applying a series of basic row operations to the circulant skew matrix so that an upper triangular matrix is obtained, followed by multiplying it with the Gamma matrix determinant. Meanwhile, the inverse formulation is obtained by making matrices from a circulant skew matrix representing the results of a series of basic row or column operations, followed by multiplying by the inverse Gamma matrix. |
URI: | http://repository.ipb.ac.id/handle/123456789/117908 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Cover.pdf Restricted Access | Cover | 587.07 kB | Adobe PDF | View/Open |
G54180032_Dwiva Mamella.pdf Restricted Access | Fulltext | 927.03 kB | Adobe PDF | View/Open |
Lampiran.pdf Restricted Access | Lampiran | 583.31 kB | Adobe PDF | View/Open |
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