A matrix decomposition method for positive semidefinite matrices based on a given subspace is proposed in this paper. It is shown that any positive semidefinite matrix can be decomposed uniquely into two positive semidefinite parts with specified rank one of which is orthogonal to the subspace. This method is then compared with the rank-additivity decomposition, and the difference as well as the close connection between these two decompositions are given. Finally, the proposed decomposition method is used to develop a new recursive parameter estimation algorithm for linear systems.

Least squares method, Matrix decomposition, Positive semidefinite matrices, Rank additivity, Recursive estimation
dx.doi.org/10.1137/S0895479899364027
SIAM Journal on Matrix Analysis and Applications
Department of Systems and Computer Engineering

Cao, L. (Liyu), & Schwartz, H.M. (2001). A decomposition method for positive semidefinite matrices and its application to recursive parameter estimation. SIAM Journal on Matrix Analysis and Applications, 22(4), 1095–1111. doi:10.1137/S0895479899364027