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Title: | Formulasi Determinan Matriks Circulant Dengan Entri Barisan Bilangan Relasi Rekurensi Orde-2 Formasi Jangkar |
Other Titles: | The Determinant Formulation of Circulant Matrix with entry of the 2nd Order Recurrence Relation Number Formasi Jangkar |
Authors: | Guritman, Sugi Mas’oed, Teduh Wulandari Sudarwan, Roni |
Issue Date: | 2022 |
Publisher: | IPB University |
Abstract: | Matriks circulant merupakan matriks segi yang entri-entri pada setiap barisnya sama dengan entri-entri pada baris sebelumnya dan bergeser posisi ke kanan. Entri-entri dari matriks circulant dapat diisi dengan berbagai entri, salah satunya adalah bilangan-bilangan yang membentuk suatu barisan bilangan. Barisan bilangan dapat dibuat dengan menggunakan relasi rekurensi orde-2. Pada karya ilmiah ini, relasi rekurensi tersebut didefinisikan sebagai \[J_{n}=2J_{n−1}+3J_{n−2}\] dengan syarat awal \[J_0=3,J_1=1,n≥2,\] dan membentuk barisan bilangan yang dinamakan Formasi Jangkar. Kemudian, determinan matriks circulant dengan entri barisan bilangan Formasi Jangkar dapat dirumuskan secara eksplisit menggunakan sifat-sifat determinan sederhana yang berkaitan dengan operasi baris dasar. The circulant matrix is a faceted matrix where the entries in each row are the same as the entries in the previous row and shift position to the right. The entries of the circulant matrix can be filled with various entries, one of which is the numbers that form a sequence of numbers. Sequences of numbers can be constructed by a recurrence relation of order-2. In this scientific work, the recurrence relation is defined as \[J_{n}=2J_{n−1}+3J_{n−2}\] with initial condition \[J_0=3,J_1=1,n≥2,\] and form a sequence of numbers called Formasi Jangkar. Then, the determinant of the circulant matrix with entry the Formasi Jangkar can be formulated eksplicitly using the properties of determinants based on elementary row operations. |
URI: | http://repository.ipb.ac.id/handle/123456789/110918 |
Appears in Collections: | UT - Mathematics |
Files in This Item:
File | Description | Size | Format | |
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Cover.pdf Restricted Access | Cover | 299.18 kB | Adobe PDF | View/Open |
G54170036-draft skripsi ter-updated.pdf Restricted Access | Fullteks | 794.78 kB | Adobe PDF | View/Open |
Lampiran.pdf Restricted Access | Lampiran | 129.16 kB | Adobe PDF | View/Open |
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