Title :
Non-symmetric matrix and unified theory of least squares
Author :
Wang, Shiqing ; Ma, Ying ; Feng, Zhijun
Author_Institution :
Coll. of Math. & Inf. Sci., North China Univ. of Water Resources & Electr. Power, Zhengzhou, China
Abstract :
Unified theory of least squares was given by Rao (1971, 1972, 1973) and Rao and Mitra (1971). In the generalized inverse (g-inverse) matrix (R + XGX·)- involved in unified theory of least squares, G is any symmetric matrix. We give the properties with matrix quadratic form of non-symmetric matrix, and extend symmetric matrix G to an arbitrary square matrix. i.e. G is not necessarily symmetric only if matrix XGX· is symmetric.
Keywords :
inverse problems; least squares approximations; matrix algebra; arbitrary square matrix; g-inverse matrix; generalized inverse matrix; matrix quadratic form; nonsymmetric matrix; unified theory of least squares; Education; best linear unbiased estimate; general Gauss - Markoff model; generalized inverse matrix; unified theory of least square;
Conference_Titel :
Computer Application and System Modeling (ICCASM), 2010 International Conference on
Conference_Location :
Taiyuan
Print_ISBN :
978-1-4244-7235-2
Electronic_ISBN :
978-1-4244-7237-6
DOI :
10.1109/ICCASM.2010.5619229
