We write S∞ to denote the unit sphere of `, the set of all z in ` for which 〈z, z〉 = 1 (this set is often called the complex Hilbert sphere). A continuous complex-valued function f defined on the closed unit disc D := {ζ ∈ C : |ζ| ≤ 1} is said to be positive definite of order n on S∞ if, for any set of n distinct points z1, . . . , zn on S∞, the n×n matrix A with ij-entry given by f(〈zi, zj〉) i...

In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all H+(Z+)-eigenvalues of each principal sub-tensor are positive. We define two new constants associated with H+(Z+)-eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establ...

Every nonsingular totally positive m-banded matrix is shown to be the product of m totally positive one-banded matrices and, therefore, the limit of strictly m-banded totally positive matrices. This result is then extended to (bi)infinite m-banded totally positive matrices with linearly independent rows and columns. In the process, such matrices are shown to possess at least one diagonal whose ...