Many of today's problems require techniques that involve the solution of arbitrarily large systems $A\mathbf{x}=\mathbf{b}$. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor decomposition. The numerical experiments support the fact that this algorithm converges especially fast when the matrix of the linear system is Laplacian-Like. These matrices that follow the tensor structure of the Laplacian operator are formed by sums of Kronecker product of matrices following a particular pattern. Moreover, this set of matrices is not only a linear subspace it is a a Lie sub-algebra of a matrix Lie Algebra. In this paper, we characterize and give the main properties of this particular class of matrices. Moreover, the above results allow us to propose an algorithm to explicitly compute the orthogonal projection onto this subspace of a given square matrix $A \in \mathbb{R}^{N\times N}.$

翻译：当今许多问题都需要涉及任意大型系统解决方案的技术 $A\ mathbf{x mathb{b}b}$A\ mathb{b}$A\ mathb{b}$。 流行的数字方法就是所谓的贪婪一等更新值值, 其基础是特定的高温分解。 数字实验支持这样的事实: 当线性系统的矩阵是 Laplacian 类似 时, 此算法会特别快。 遵循 Laplacian 操作器的强力结构的矩阵是由根据特定模式的矩阵的Kronecker 产品构成的。 此外, 这组矩阵不仅是一个线性子空间, 而且它是一个矩阵 lie Algebra 的 Lie 子值。 在本文中, 我们描述并给出了该特定矩阵类别的主要属性 。 此外, 上述结果允许我们提出一种算法, 明确计算该矩阵在给定的平方矩阵 $A\ mathb{R\\\ times N$。