کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
473699 698805 2011 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Solutions with special structure to the linear matrix equation AX=B
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
Solutions with special structure to the linear matrix equation AX=B
چکیده انگلیسی
In this article we solve the following three kinds of problems. First, some formulas for the minimal rank of the submatrices in a solution X of matrix equation AX=B and the minimal and maximal rank of X itself are derived by using the matrix rank method. From these formulas, necessary and sufficient conditions are given for X to be nonsingular or the submatrices to be zero, respectively. Second, some formulas for the minimal rank of X+X∗, X−X∗ and the corresponding expressions of submatrices of X are investigated. Combined with matrix decomposition, necessary and sufficient conditions are given for the existence of solutions to be Hermitian, local Hermitian, Skew-Hermitian and local Skew-Hermitian, respectively. Third, necessary and sufficient conditions are given for the existence of solutions to be local positive (negative) semidefinite, and for some Hermitian solution with zero submatrix, the structure form of a positive (negative) semidefinite solution are obtained using results of inertia.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 61, Issue 2, January 2011, Pages 374-383
نویسندگان
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