Karakteristik Matriks-P

VELIXIA SOFIA JELO , Dr. Diah Junia Eksi Palupi, M.S.

2018 | Skripsi | S1 MATEMATIKA

Suatu matriks A berukuran n x n atas R dapat dipartisi menjadi beberapa submatriks. Submatriks terpartisi atas submatriks biasa dan submatriks utama. Determinan submatriks utama matriks A disebut nilai minor utama matriks A. Suatu matriks A dikatakan matriks-P jika setiap nilai minor utama matriks A bernilai positif. Jika jumlahan setiap nilai minor utama matriks A bernilai positif maka matriks A disebut matriks-Q. Apabila matriks A dan A2 merupakan matriks-P maka matriks A merupakan matriks-P2. Submatriks matriks A yang merupakan matriks-P dapat digunakan untuk menentukan Schur complements, nested sequence, dan compound matrix matriks A. Pada skripsi ini akan dibahas mengenai karakteristik matriks-P antara lain hubungan matriks-P dengan beberapa matriks seperti matriks sign-symmetric, matriks-Q dan matriks-P2 juga hubungan matriks-P2 yang mempunyai suatu nested sequence submatriks utama dengan compound matrix.

A real n x n matrix A can be partitioned to be several submatrices. Those submatrices are partitioned into ordinary submatrix and principal submatrix. The determinant of a principal submatrix of matrix A can be considered as a principal minor of matrix A. A matrix A can be regarded as P-matrix if each of principal as minor of matrix A is positive. If the sum of a principal minor of matrix A is positive then matrix A is called Q-matrix. If matrix A and A2 are P-matrix then matrix A can be considered P2-matrix. A submatrix of matrix A which is P-matrix can be used to determine the Schur complements, nested sequence, and the compound matrix of matrix A. This graduating paper discusses the characteristic of P-matrices such as the relationship between the P-matrices and several matrices like the sign-symmetric matrix, Q-matrix, and P2-matrix and the relationship of P2-matrix which have a nested sequence with the compound matrix.

Kata Kunci : Matriks, matriks-P, submatriks, determinan, nilai minor utama.