Appendix Properties of positive (semi)definite matricesde Klerk, Etienne
Determinants and matrices are used to solve the system of linear equations. Learn its definition, types, properties, matrix inverse, transpose with more examples at BYJU’S.
Positive semidefinite matricesDensity matricesProjectionsWe use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or R茅nyi entropy. ...
The frame synthesis matrix H∈Cm×N consists of the concatenated frame vectors H=[h1h2…hN]. The Gram matrix of the frame H is denoted G=HHH and has several special properties: it is Hermitian and positive semidefinite, it has ones along the diagonal and the off-diagonal entries are equal...
According to Yuan, there exists a convex combination of these matrices which is positive semidefinite, if and only if the function x ∈ R n max { x T A 1 x , x T A 2 x } is nonnegative. We study the case in which more than two matrices are involved. We study also a related ...
Moreover, if the Hermitian matrix to be recovered is known to be positive semidefinite, then we show that the nuclear norm minimization approach may be replaced by minimizing the lq-norm of the residual subject to the positive semidefinite constraint (e.g. by a positive semidefinite least ...
Likewise, M ∈ Rn×n belongs to the class of positive semidefinite matrices (P S D) if xT Mx ≥ 0 holds for all x ∈ Rn. Furthermore, M ∈ Rn×n is a skew-symmetric matrix (SS), if xT Mx = 0 for all x ∈ Rn. Clearly, the decision problem of whether the matrix is skew-...
Infinitely divisible matricesPositive semidefinite matricesSchur productStirling numbersTotally positive matricesThe beta functionIt is shown that for positive real numbers 0 < lambda(1) < ... < lambda(n), [1/beta(lambda i,lambda j)], where beta(.,.) denotes the beta function, is infinitely ...
Li, Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices, Math. Comput., 76(2007), 287-298.Z.-Z. Bai, G.H. Golub, and C.-K. Li, Convergence properties of preconditioned Hermitian and skew-Hermitian splitting ...
[Math Processing Error]A⪰0 and [Math Processing Error]A≻0 respectively denote that A is positive semidefinite and positive definite. [Math Processing Error]Sn, [Math Processing Error]S⪰0n, and [Math Processing Error]S≻0n are the sets of n-dimensional symmetric matrices, positive ...