Determinan dan Invers Matriks Skew Circulant dengan Entri Bilangan Pell
Abstract
Matriks skew circulant adalah matriks persegi yang entrinya bergeser satu kolom ke kanan secara berurutan dengan seluruh entri sebelum diagonal utama akan bernilai negatif. Entri-entri dari matriks skew circulant dapat diisi dengan entri berbagai bilangan, salah satunya yaitu bilangan Pell. Pada karya ilmiah ini, determinan dan invers matriks skew circulant dengan entri bilangan Pell diformulasikan. Pembuktian formulasi determinan matriks skew circulant dengan entri bilangan Pell dilakukan berdasarkan serangkaian operasi baris dasar sehingga diperoleh matriks segitiga atas. Sedangkan pembuktian formulasi pada inversnya berlandaskan sifat-sifat ekuivalensi dari hasil kombinasi operasi baris dasar dan operasi kolom dasar. Skew circulant matrix is a square matrix whose entries are shifted one column to the right and all entries before the main diagonal will be negative.The entries of the circulant skew matrix can be filled in various numbers, one of which is the Pell number. In this scientific work, the determinant and inverse of skew circulant matrices with the entry of the Pell number are formulated. The substantiation of the determinant formulation of the circulant skew matrix with the entry of the Pell numbers is carried out on the basis of a series of elementary row operations so that an upper triangular matrix is obtained. Meanwhile, the proof of the formulation in the inverse is based on the equivalence proprties of the results of a combination of elementary row and column operations.
Collections
- UT - Mathematics [1432]