線性代數(shù)

內容概要

　　隨著計算機技術的發(fā)展，線性代數(shù)課程的重要性越來越突出。同時，現(xiàn)代軟件已經(jīng)為顯著改進授課方式提供了可能。本書作者多年講授線性代數(shù)課程，并在教學過程中不斷探索更利于學生理解的新教學方法，從而使本書更加適合作為線性代數(shù)課程的教材。
　　在第8版中，擴充了矩陣代數(shù)的知識，新增了向量積、實舒爾分解的內容，并增加了130多道新練習。
　　本書主要特點
　　? 理論與應用有機結合。大量的實際應用貫穿于理論講解的始終，體現(xiàn)了線性代數(shù)在各個領域中的廣泛應用。
　　? 示例豐富。便于讀者理解相關的定義及原理，增強了讀者學習的興趣。
　　? 習題安排錯落有致。每一節(jié)的后面給出大量的習題，各章后面還有測試題，使學生有更多的演練機會，達到觸類旁通的效果。
　　? 緊密結合數(shù)學工具MATLAB。每章的后面都有基于MATLAB的上機練習，并在附錄中介紹了MATLAB的基本用法。

作者簡介

　　Steven J. Leon
1971年于密歇根州立大學數(shù)學系獲得博士學位，現(xiàn)為馬薩諸塞大學達特茅斯分校數(shù)學系首席教授，ILAS（國際線性代數(shù)協(xié)會）、MAA（美國數(shù)學學會）和SIAM（美國工業(yè)與應用數(shù)學協(xié)會）成員。他主要從事科學計算、線性代數(shù)和應用數(shù)學等領域的研究。

書籍目錄

preface
matrices and systems of equations
 1.1 systems of linear equations
 1.2 row echelonform
 1.3 matrix arithmetic
 1.4 matrix algebra
 1.5 elementary matrices
 1.6 partitioned matrices
 matlab r exercises
 chaptertesta
 chaptertestb
2 determinants
 2.1 the determinant of a matrix
 2.2 properties of determinants
 2.3. additionaltopics and applications
 matlab exercises
 chaptertesta
 chaptertestb
3 vector spaces
 3.1 definition and examples
 3.2 subspaces
 3.3 linear independence
 3.4 basis and dimension
 3.5 change of basis
 3.6 row space and column space
 matlab exercises
 chaptertesta
 chaptertestb
4 linear transformations
 4.1 definition and examples
 4.2 matrix representationsof lineartransformations
 4.3 similarity
 matlab exercises
 chaptertesta
 chaptertestb
5 orthogonality
 5.1 the scalar product in rn
 5.2 orthogonal subspaces
 5.3 least squares problems
 5.4 inner product spaces
 5.5 orthonormal sets
 5.6 the gram–schmidt orthogonalization process
 5.7 orthogonal polynomials
 matlab exercises
 chaptertesta
 chaptertestb
6 eigenvalues
 6.1 eigenvalues and eigenvectors
 6.2 systems of linear differential equations
 6.3 diagonalization
 6.4 hermitian matrices
 6.5 the singularvalue decomposition
 6.6 quadraticforms
 6.7 positive definite matrices
 6.8 nonnegative matrices
 matlab exercises
 chaptertesta
 chaptertestb
7 numerical linear algebra
 7.1 floating-point numbers
 7.2 gaussian elimination
 7.3 pivoting strategies
 7.4 matrix norms and condition numbers
 7.5 orthogonal transformations
 7.6 the eigenvalue problem
 7.7 least squares problems
 matlab exercises
 chapter test a
 chapter test b
8 iterative methods web.
9 canonical forms web.
appendix: matlab
bibliography
answers to selected exercises
index

章節(jié)摘錄

版權頁：插圖：The first column of the table indicates the distribution of the goods produced by the farmers, the second column indicates the distribution of the manufactured goods, and the third column indicates the distribution of the clothing.As the size of the tribe grows, the system of bartering becomes too cumbersome and, consequently, the tribe decides to institute a monetary system of exchange. For this simple economic system, we assume that there will be no accumulation of capital or debt and that the prices for each of the three types of goods will reflect the values of the existing bartering system. The question is how to assign values to the three types of goods that fairly represent the current bartering system.The problem can be turned into a linear system of equations using an economic model that was originally developed by the Nobel Prize-winning economist Wassily Leontief. For this model, we will let xl be the monetary value of the goods produced by the farmers, x2 be the value of the manufactured goods, and x3 be the value of all the clothing produced. According to the first row of the table, the value of the goods received by the farmers amounts to half the value of the farm goods produced, plus one-third the value of the manufactured products and half the value of the clothing goods.

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