Some new matrix versions of Kantorovich-Type inequalities for Hermitian matrix are proposed in this paper. We consider what happens to these inequalities when the positive definite matrix is allowed to be positive semidefinite singular or indefinite.

We show that the three-dimensional (3-D) motion parameters of a rigid planar patch can be determined by computing the singular value decomposition (SVD) of a 3 X 3 matrix containiig the eight so called “pure parameters.” Furthermore, aside from a scale factor for the translation parameters, the number of solutions is either one or two, depending on the multiplicity of the singular values of the...

We give upper and lower bounds on the largest singular value of a matrix using analogues to walks in graphs. For nonnegative matrices these bounds are asymptotically tight. In particular, the following result improves a bound due to Schur. If A = (aij) is an m× n complex matrix, its largest singular value satisfies σ (A) ≤ max i∈[m] ∑ j∈[n] |aij| cj ≤ max aij 6=0 ricj, where ri = ∑ k∈[n] |aik| ...