论文标题
矩阵分解和应用
Matrix Decomposition and Applications
论文作者
论文摘要
1954年，Alston S. Houseperer发表了数值分析原理，这是基质分解的首批现代疗法之一，其中有利于A（块）LU分解 - 将基质分解为下层和上三角矩阵的产物。而现在，矩阵分解已成为机器学习的核心技术，这主要是由于拟合神经网络的反向传播算法的发展。该调查的唯一目的是在数值线性代数和矩阵分析中对概念和数学工具进行独立介绍，以便在随后的部分中无缝介绍矩阵分解技术及其应用。但是，鉴于范围很少提出这一讨论的范围，例如，我们无法涵盖有关基质分解的所有有用且有趣的结果，例如，对欧几里得空间，Hermitian空间，希尔伯特空间以及复杂领域中事物的分开分析。我们将读者推荐给线性代数领域的文献，以更详细地介绍相关字段。
In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the backpropagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition, given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.
