Author
Lizhu Sun
Bio: Lizhu Sun is an academic researcher from Harbin Institute of Technology. The author has contributed to research in topics: Tensor & Invariants of tensors. The author has an hindex of 5, co-authored 10 publications receiving 205 citations.
Papers
More filters
TL;DR: In this article, the Moore-Penrose inverse of tensors with the Einstein product is defined and the explicit formulas of the MPN inverse of some block tensors are obtained.
Abstract: In this paper, we define the Moore–Penrose inverse of tensors with the Einstein product, and the explicit formulas of the Moore–Penrose inverse of some block tensors are obtained. The general solutions of some multilinear systems are given and we also give the minimum-norm least-square solution of some multilinear systems using the Moore–Penrose inverse of tensors.
120 citations
TL;DR: In this paper, an application of resistance distances to the bipartiteness of graphs is given, and an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix is given.
Abstract: In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix.
59 citations
TL;DR: By using digraphs of tensors, the authors gave Brualdi-type eigenvalue inclusion sets for tensors and also gave some applications of their result to nonsingularity and positive definiteness.
40 citations
TL;DR: For a tensor A = (a i 1 ⋯ i m ) ∈ C n × ⋩ × n, the associated digraph of A has the vertex set V ( A ) = { 1, …, n }, and the arc set of Γ A is E ( A) = { ( i, j ) | a i i 2 ⋌ i m ≠ 0, j ∈ { i 2, …, i m } ≠ { i, …-, i m ∈ [ i,, j ] ≠
11 citations
TL;DR: In this paper, the explicit formulas for the Drazin inverse of the block matrices were given when $PQ^2 = 0, $P^2QP = 0.
Abstract: Let $\mathbb{K}$$^{m \times n}$ be the set of all the $m\times n$ matrices over the skew field. For the matrices $P,~Q \in $$\mathbb{K}$$^{n \times n}$, the explicit formulas for the Drazin inverse of $P + Q$ are given when $PQ^2 = 0$, $P^2QP = 0$, $(QP)^2 = 0$ and $P^2 QP = 0$, $P^3 Q = 0$, $Q^2 = 0$, respectively. Using these formulas, the representations for the Drazin inverse of the block matrices $ \left( {\begin{array}{*{20}c} A & B \\ C & D \\ \end{array} } \right)\in\mathbb{K}^{n \times n}$ are showed with some conditions, where $A$ and $D$ are square.
9 citations
Cited by
More filters
[...]
TL;DR: In this paper, the adjacency matrix, a matrix of O's and l's, is used to store a graph or digraph in a computer, and certain matrix operations are seen to correspond to digraph concepts.
Abstract: In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.
292 citations
TL;DR: This paper characterize the graph having the minimum Kf(G) values among graphs with a fixed number n of vertices and fixed vertex bipartiteness, 1 ź v b ź n - 3 .
111 citations
TL;DR: In this paper, a generalized tensor function according to the tensor singular value decomposition (T-SVD) is defined, from which the projection operators and Moore-Penrose inverse of tensors are obtained.
81 citations
26 May 2021
TL;DR: In this article, the T-Jordan canonical form and its properties are investigated for tensor similarity and the concepts of Tminimal polynomial and T-characteristic polynomials are proposed.
Abstract: In this paper, we investigate the tensor similarity and propose the T-Jordan canonical form and its properties. The concepts of the T-minimal polynomial and the T-characteristic polynomial are proposed. As a special case, we present properties when two tensors commute based on the tensor T-product. We prove that the Cayley–Hamilton theorem also holds for tensor cases. Then, we focus on the tensor decompositions: T-polar, T-LU, T-QR and T-Schur decompositions of tensors are obtained. When an F-square tensor is not invertible with the T-product, we study the T-group inverse and the T-Drazin inverse which can be viewed as the extension of matrix cases. The expressions of the T-group and T-Drazin inverses are given by the T-Jordan canonical form. The polynomial form of the T-Drazin inverse is also proposed. In the last part, we give the T-core-nilpotent decomposition and show that the T-index and T-Drazin inverses can be given by a limit process.
67 citations