普通高等教育“十三五”规划教材普通高等院校数学精品教材线性代数英文_毛纲源马迎秋梁敏编著；米洪海丛书主编.pdf

丛书编委会主编米洪海毛纲源副主编孙洪波侯健高洁编委(按姓氏笔画排序)马迎秋毛纲源米洪海孙洪波周海婴侯健徐丽莉高洁梁敏Linear AlgebraTriangular MatrixSymmetric MatrixOrthogonal Matrix1111231/W21/W61/W30-1-112-561W21/W61/W30-3-23-51700-146-72/W61/53.The Structure of this BookThis book organizes the content basis on the logical relationship amongnumber,matrix and vector.It lists the structure from determinant,to matrix,tosolve system of linear equations,to vector,to structure of solutions,to eigenvalueand eigenvector,to quadratic form finally.Here is the structure of this book:Chapter 1 starts with determinant.There are three important points about thedeterminant.The first is the definition,the second is property,and the last is itsexpansion.The Cramers rule is given basis on these three points.Chapter 2 gives all the varieties of matrix.After the study of concept ofmatrix,it begins with algebra operations,and shows some special matrices.It isfollowing with how to partition matrix,and how to find the inverse of matrix.After given the elementary operations and elementary matrix,this chapter is endedby rank of matrix.Chapter 3 shows the relationship between matrix and the system of linearequations.Certainly,it is the most important that using matrix to solve the systemof linear equations.Gaussian Elimination Method is the most helpful technique.Chapter 4 begins studying vector.Definition and operation are two basic studypoints.Linear dependence and rank of vector are two new knowledge structures.Chapter 5 is mainly basis on chapter 3 and chapter 4.Here is similarframework for giving the structure of solutions of homogeneous andnonhomogeneous system of linear equations.Both these two parts discuss thecorresponding property firstly,and give the details of their structure respectively.Chapter 6 is mostly in eigenvalue and eigenvector.Besides the definition ofthem,there are.three points of matrix using both two of them which arediagonalization,similar matrix and real symmetric matrix.Chapter 7 is quadratic form which has three points.The first point is about the