In this paper, we study two classes of quasi-double diagonally dominant tensors and prove they are H-tensors. Numerical examples show that H-tensors mutually exclusive. Thus, extend the decision conditions Based on these tensors, estimation inequalities for upper lower bounds spectral radius nonnegative obtained.

Introduction Diffusion tensor imaging (DTI) has been widely used to construct the orientation and structure of fibers in biological tissues, particularly in the white matter of the brain [1]. The raw diffusion-weighted images (DWI) from which diffusion tensors are estimated, however, inherently contain large amounts of noise, leading to uncertainty in the estimation of the tensors and their der...

In many engineering applications that use tensor analysis, such as tensor imaging, the underlying tensors have the characteristic of being positive definite. It might therefore be more appropriate to use techniques specially adapted to such tensors. We will describe the geometry and calculus on the Riemannian symmetric space of positive-definite tensors. First, we will explain why the geometry,...

Strong [Formula: see text]-tensors play an important role in identifying the positive definiteness of even-order real symmetric tensors. In this paper, some new iterative criteria for identifying strong [Formula: see text]-tensors are obtained. These criteria only depend on the elements of the tensors, and it can be more effective to determine whether a given tensor is a strong [Formula: see te...

We show that the space of algebraic covariant derivative curvature tensors R is generated by Young symmetrized product tensors T ⊗ T̂ or T̂ ⊗ T , where T and T̂ are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2), (3)}, {(2), (2 1)} or {(1), (2 1)}. Each of the partitions (2), (3) and (1) describes exactly one s...

Though algebraic geometry over C is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the n × n × n tensors of rank n over C, which has as a dense subset the orbit of a single tensor under a natural group action. We construct polynomial invariants under this group action whose non-v...

Tensors model a wide range of physical phenomena. While symmetric tensors are sufficient for some applications (such as diffusion), asymmetric tensors are required, for example, to describe differential properties of fluid flow. Glyphs permit inspecting individual tensor values, but existing tensor glyphs are fully defined only for symmetric tensors. We propose a glyph to visualize asymmetric s...

With the notable exceptions of two cases — that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-one approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption that only one set...

Orientation tensors is a powerful representation of local orientation. Over the years, several different approaches to estimate the tensors have appeared. The derivations of the different tensors vary to a great extent. This partly obstructs a theoretical comparison between them, which otherwise would be useful when one wants to choose the best tensor for a particular application. This paper sh...

We present a new method of deriving microstructure-dependent bounds on the effective properties of general heterogeneous media. The microstructure is specified by the average Eshelby tensors. In the small contrast limit, we introduce and calculate the expansion coefficient tensors. We then show that the effective tensor satisfies a differential inequality with the initial condition given by the...