Factorization on totally positive sign equivalent matrices

 By : Aleksander Hutauruk, Drs,M.Si

 Supported by : Muhafzan,P.Hd & Jenizon,M.Si 

                                                     ABSTRACS  

         Factorization of matrices is the multiply of matrices which is suitable with   where A is as input matrix and  ,  is as factorial matrices that is matrices suitable with in a certain condition. The number of k represents the number of factorial matrix F.

Factorization on totally positive sign equivalent matrices that the matrices being able to be D₁QD₂, with Q is totally positive matrix, D₁ and D₁ are diagonal matrices with main diagonal elements equal to +1 or -1.

 Theorem in factorization on totally positive sign equivalent matrices that every square real matrix n x n, n ≥ 2 is result of multiplical totally positive sign equivalent matrices, indicated and stated based on facts in Lowner-Neville factorization, the concept about matrix and facorization matrix. One of them is facorization : Cholesky, LU, and QR.

 Keywords:  

Totally positive matrix, Totally positive sign equivalent matrix, Factorization on totally positive sign equivalent matrix, Lowner-Neville factorization.