線性代數(shù)

內(nèi)容概要

　　隨著計(jì)算機(jī)技術(shù)的發(fā)展，線性代數(shù)課程的重要性越來(lái)越突出。同時(shí)，現(xiàn)代軟件已經(jīng)為顯著改進(jìn)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(xué)過(guò)程中不斷探索更利于學(xué)生理解的新教學(xué)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(kuò)充了矩陣代數(shù)的知識(shí)，新增了向量積、實(shí)舒爾分解的內(nèi)容，并增加了130多道新練習(xí)。
　　本書主要特點(diǎn)
　　? 理論與應(yīng)用有機(jī)結(jié)合。大量的實(shí)際應(yīng)用貫穿于理論講解的始終，體現(xiàn)了線性代數(shù)在各個(gè)領(lǐng)域中的廣泛應(yīng)用。
　　? 示例豐富。便于讀者理解相關(guān)的定義及原理，增強(qiáng)了讀者學(xué)習(xí)的興趣。
　　? 習(xí)題安排錯(cuò)落有致。每一節(jié)的后面給出大量的習(xí)題，各章后面還有測(cè)試題，使學(xué)生有更多的演練機(jī)會(huì)，達(dá)到觸類旁通的效果。
　　? 緊密結(jié)合數(shù)學(xué)工具M(jìn)ATLAB。每章的后面都有基于MATLAB的上機(jī)練習(xí)，并在附錄中介紹了MATLAB的基本用法。

作者簡(jiǎn)介

　　Steven J. Leon
1971年于密歇根州立大學(xué)數(shù)學(xué)系獲得博士學(xué)位，現(xiàn)為馬薩諸塞大學(xué)達(dá)特茅斯分校數(shù)學(xué)系首席教授，ILAS（國(guó)際線性代數(shù)協(xié)會(huì)）、MAA（美國(guó)數(shù)學(xué)學(xué)會(huì)）和SIAM（美國(guó)工業(yè)與應(yīng)用數(shù)學(xué)協(xié)會(huì)）成員。他主要從事科學(xué)計(jì)算、線性代數(shù)和應(yīng)用數(shù)學(xué)等領(lǐng)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(quán)頁(yè)：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.

編輯推薦

《線性代數(shù)(英文版?第8版)》是華章數(shù)學(xué)原版精品系列之一。

圖書封面

圖書標(biāo)簽Tags

無(wú)

評(píng)論、評(píng)分、閱讀與下載

---

    線性代數(shù) PDF格式下載

---