Sparse Recovery on Euclidean Jordan Algebras

We consider the sparse recovery problem on Euclidean Jordan algebra (SREJA), which includes sparse signal recovery and low-rank symmetric matrix recovery as special cases. We introduce the restricted isometry property, null space property (NSP), and $s$-goodness for linear transformations in $s$-sparse element recovery on Euclidean Jordan algebra (SREJA), all of which provide sufficient conditions for … Read more

Lowest-rank Solutions of Continuous and Discrete Lyapunov Equations over Symmetric Cone

The low-rank solutions of continuous and discrete Lyapunov equations are of great importance but generally difficult to achieve in control system analysis and design. Fortunately, Mesbahi and Papavassilopoulos [On the rank minimization problems over a positive semidefinite linear matrix inequality, IEEE Trans. Auto. Control, Vol. 42, No. 2 (1997), 239-243] showed that with the semidefinite … Read more

On the bilinearity rank of a proper cone and Lyapunov-like transformations

A real square matrix Q is a bilinear complementarity relation on a proper cone K in R^n if x in K, s in K^* with x perpendicular to s implies x^{T}Qs=0, where K^* is the dual of K. The bilinearity rank of K is the dimension of the space of all bilinear complementarity relations on … Read more