Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

Tensors, as geometric objects that describe linear or multi-linear relations between
geometric vectors, scalars, and other tensors, have provided a concise mathematical …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

Simplicial complexes are mathematical constructions that describe higher-order interactions
within the interconnecting elements of a network. Such higher-order interactions become …

Tensors (hypermatrices) are multidimensional analogs of matrices. The tensor
complementarity problem is a class of nonlinear complementarity problems with the involved …

In order to process the large-scale data, a useful tool in dimensionality reduction of a matrix,
the CUR decomposition has been developed, which can compress the huge matrix with its …

The notion of the Moore–Penrose inverse of a matrix has been extended to tensor case with
Einstein product, recently. In this paper, we continue this work and propose the full rank …

Tensor systems involving tensor-vector products (or polynomial systems) are considered.
We solve these tensor systems, especially focusing on symmetric M M-tensor systems, by …

With the coming of the big data era, high-order high-dimensional structured tensors received
much attentions of researchers' in recent years, and now they are developed into a new …

Specific definitions of the core and core-EP inverses of complex tensors are introduced.
Some characterizations, representations and properties of the core and core-EP inverses …