python高维数据分析（英文版）.pptxVIP

第1章.pptxChapter1 BasisofMatrixCalculatio第2章.pptxChapter2 TheSolutionofLeastSquaresProblems第3章.pptxChapter3 PrincipalComponentAnalysi第4章.pptxChapter4 PartialLeastSquaresAnalysis第5章.pptxChapter5 Regularizatio第6章.pptxChapter6 TransferMethodcontents目录Chapter1 Basis of Matrix Calculation1.1 Fundamental Concepts1.2 The Most Basic Matrix Decompositio1.3 Singular Value Decomposition(SVD)1.4 The Quadratic Form1.1 FundamentalConcepts　The purpose of this chapter is to review important fundamental concepts in linear algebra, as a foundation for the rest of the course.We first discuss the fundamental building blocks,such asan overview of matrix multiplicationfrom a “big block” perspective, linear independence, subspaces and related ideas,rank,etc.,upon which the rigor of linear algebra rests. We then discuss vector norms,and various interpretations of the matrix multiplication operation1.1.1 Notation Throughout this course, we shall indicate that a matrix A is of dimensionm×n,and whose elements are taken from the set of real numbers,by then otation A∈Cm×n .This means that the matrix A belongs to the Cartesian product of the real numbers, taken m×n times, one for each element of A. In a similar way, the notation A ∈Cm×n means the matrix is of dimension m×n, and the elements are taken from the set of complex numbers. By the matrix dimension m×n, we mean A consists of m rows and ncolumns. Similarly,the notation a∈Rm (Cm ) implies a vector of dimension m whose elements are taken from the set of real (complex) numbers. By “dimension of a vector”,we mean its length,i.e.,that it consists of m elements. Also,we shall indicate that a scalar a is from the set of real(complex)numbers by the notation a∈R(C). Thus, an upper case bold character denotes a matrix, a lower case bold character denotes a vector,and a lower casenon-bold character denotes a scalar. By convention, a vector by default is taken to be a column vector. Further,for a matrix A, we denote its i-th column as ai. We also