- A NOTE ON PARTIAL SIGN-SOLVABILITY
- A NOTE ON PARTIAL SIGN-SOLVABILITY
- ㆍ 저자명
- Hwang. Suk-Geun,Park. Jin-Woo
- ㆍ 간행물명
- Bulletin of the Korean Mathematical Society
- ㆍ 권/호정보
- 2006년|43권 3호|pp.471-478 (8 pages)
- ㆍ 발행정보
- 대한수학회
- ㆍ 파일정보
- 정기간행물|ENG| PDF텍스트
- ㆍ 주제분야
- 기타
In this paper we prove that if AX=b is a partial sign-solvable linear system with A being sign non-singular matrix and if ${alpha}={j:;x_j;is;sign-determined;by; Ax=b}, then $A_{alpha}X_{alpha}=b_{alpha}$ is a sign-solvable linear system, where $A_{alpha}$ denotes the submatrix of A occupying rows and columns in o and xo and be are subvectors of x and b whose components lie in ${alpha}$. For a sign non-singular matrix A, let $A_l,;...,A_{kappa}$ be the fully indecomposable components of A and let ${alpha}_i$ denote the set of row numbers of $A_r,;r=1,;...,;k$. We also show that if $A_x=b$ is a partial sign-solvable linear system, then, for $r=1,;...,;k$, if one of the components of xor is a fixed zero solution of Ax=b, then so are all the components of x_{{alpha}r}$.