线性代数及其在矩阵分析中的应用

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 higher order generalization of a matrix, the concept of tensors or hypermatrices has been introduced and studied due to multi-indexed data sets from wide applications in scientific and engineering communities. With more subscripts, compared to matrices, tensors possess their own geometric and algebraic structures which might be lost if we reshape or unfold them into matrices. One of their intrinsic features that heavily relies on the tensor structures is the concept of tensor eigenvalues, which turns out to be much more complex than that of the matrix case. Thus, tensors must then be treated as data objects in their own right, and theory on this new type of objects is required, while matrix analysis is still of importance but less so.