A Real-Valued Spectral Decomposition of the Undamped Gyroscopic System with Applications
Zhigang Jia, Musheng Wei · SIAM Journal on Matrix Analysis and Applications · 2011
Given an undamped gyroscopic system [Formula: see text] with [Formula: see text], [Formula: see text] symmetric and [Formula: see text] skew-symmetric, this paper presents a real-valued spectral decomposition of [Formula: see text] by a real standard pair [Formula: see text] and a skew-symmetric parameter matrix [Formula: see text]. When [Formula: see text] is assumed to be a block diagonal matrix, the parameter matrix [Formula: see text] has a special structure. This spectral decomposition is applied to solve the quadratic inverse eigenvalue problem and the no spill-over quadratic eigenvalue updating problem.