In this paper, some new upper bounds on the spectral radius of the Hadamard product of two nonnegative matrices and some upper and lower bounds on the spectral radius of the iterative matrix of a nonsingular M-matrix are given.
This method is convergent when the coefficient matrix is a nonsingular M-matrix.
matrix is a nonsingular M-matrix (e.g., see [[1], Lemma 3.2]).
Therefore, is an M-matrix if ; a nonsingular M-matrix if or is irreducible and, whence it is copositive, strictly copositive, respectively by [1, Theorem ].
Since the regularized matrix is a nonsingular symmetrical positive definite matrix, we can use a Choleski factorization, providing an upper triangular matrix satisfying the relation, to efficiently compute the least-squares solution (B4).
A nonsingular -matrix [7] is a -matrix (i.e., all its off-diagonal elements are nonpositive) with nonnegative inverse, and a matrix is an -matrix if and only if its comparison matrix is a nonsingular -matrix, where.
It is known that, for every matrix, there exists a nonsingular matrix transforming it to the corresponding Jordan matrix form.
In practical applications, we sometimes consider the first-order linear homogeneous matrix difference equation begin{aligned} vec{x}_{i-1} = mathbf{A} vec{x}_{i} end{aligned} (17) instead of (4), where the transition matrix A is a nonsingular matrix of (mathbf{C}^{n times n}).
Similarly, applying the ABdC-N scheme (4) to calculate the value of the (k+2 th time layer, the coefficient matrix (E+D_{2}G) of this matrix equation is also a nonsingular matrix.
Lemma 3.2 Under hypothesis (H3), matrix Γ is a nonsingular M-matrix.
