INVERS MOORE-PENROSE PADA MATRIKS ATAS ALJABAR MAX-PLUS TERSIMETRI

Suroto Suroto

Sari


Pada makalah ini dibahas tentang invers Moore-Penrose pada matriks atas aljabar max-plus tersimetri. Pendefinisian invers Moore-Penrose atas aljabar max-plus tersimetri dilakukan dengan mengadopsi invers Moore-Penrose pada aljabar konvensional. Relasi “sama dengan” pada aljabar konvensional diganti peranannya dengan relasi “setimbang” pada aljabar max-plus tersimetri. Eksistensi invers Moore-Penrose ditunjukkan dengan memanfaatkan suatu fungsi yang mengkorespondensikan aljabar max-plus tersimetri dengan aljabar konvensional. Hasil yang diperoleh adalah bentuk dan beberapa sifat invers Moore-Penrose pada matriks atas aljabar max-plus tersimetri. Hasil ini berpotensi dapat dimanfaatkan untuk menentukan solusi dari sistem kesetimbangan linier atas aljabar max-plus tersimetri yang memiliki kemiripan peranan dengan sistem persamaan linier pada aljabar konvensional.Kata kunci: Aljabar max-plus tersimetri, invers Moore-Penrose, matriks

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DOI: http://dx.doi.org/10.25157/teorema.v6i2.5514

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