A decomposition method for positive semidefinite matrices and its application to recursive parameter estimation (Q2706309)

The authors deal with the problem to decompose a positive semidefinite matrix \(A\) into a sum of two positive semidefinite matrices \(B\) and \(C,\) \(A=B+C,\) subject to certain rank and orthogonality conditions. They call this an orthogonal decomposition along a subspace. They show that it has the rank additivity property, \(\text{rank} A=\text{rank} B+\text{rank} C.\) This decomposition is then used to develop a new recursive parameter estimation algorithm for linear systems.