*Notation and Mathematical Symbols*

If *M* is a square Hermitian matrix, then *M* 0 denotes that it is positive definite and *M*0 denotes it is positive semidefinite. Also, *M* ≺ 0 denotes, that it is negative definite.

$$\mathbf{Z}\_{0+} = \{ z \in \mathbf{Z} \, :\, z \ge 0 \}; \, \mathbf{Z}\_{+} = \{ z \in \mathbf{Z} \, :\, z > 0 \},$$

$$\mathbf{R}\_{0+} = \{ z \in \mathbf{R} \, :\, z \ge 0 \}; \, \mathbf{R}\_{+} = \{ z \in \mathbf{R} \, :\, z > 0 \},$$

$$\mathbf{C}\_{0+} = \{ z \in \mathbf{C} \, : \, \text{Re} \, z \ge 0 \}; \, \mathbf{C}\_{+} = \{ z \in \mathbf{C} \, : \, \text{Re} \, z > 0 \},$$

$$\overline{n} = \{ 1, 2, \dots, n \}$$

*I* is an identity matrix specified by *In* if it denotes the *n*-th identity matrix, *A* 0 denotes that the square matrix *A* is positive definite (positive semidefinite), *A* ≺ 0 denotes that the square matrix *A* is negative definite (respectively, negative semidefinite), *A B*, *A B*, *A* ≺ *B*, *A* ≺*B* denote, respectively, that *A* −*B* 0, *A* −*B*0, *A* −*B* ≺ 0 and *A* −*B*≺0, <sup>λ</sup>min(*M*) and <sup>λ</sup>max(*M*) denote, respectively, the minimum and maximum eigenvalue of a square real symmetric matrix *M*, *r*(*M*) is the spectral radius of any square complex matrix *M*, *sp*(*M*) is the set of eigenvalues of the Hermitian matrix *M*. If such a set is ordered with respect to the partial order relation " ≤ " then the ordered spectrum is

denoted by *sp*≤(*M*). The superscripts \* and *T* stand, respectively, for complex conjugates or transposes of any vector or matrix, *A* ⊗ *B* is the Kronecker product of the matrices *A*, if *A* ∈ **C***<sup>n</sup>*×*<sup>m</sup>* then its vectorization is a vector *vec*(*A*) ∈ **C***<sup>n</sup>*×*<sup>m</sup>* whose components are all the rows of *A* written in column in its order and respecting the order of its respective entries, *A*† is the Moore-Penrose pseudoinverse of the matrix *A*.
