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Introductory Linear Algebra  무료배송

 
지은이 : Ki-BongNam, Xueqing Chen, In Sook Ma, Moon-Ok Wang, Ki-Suk Lee
출판사 : 경문사
판수 : 1판(2012 )
페이지수 : 406
ISBN : 978-89-6105-490-4
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
   

 
This book is intended as a basic textbook for students in their freshman or sophomore year. Calculus is not a prerequisite. However students with a cal-culus background may extend several concepts of this book. Many examples
and simple exercises are included to help students, since the material can not truly be learned without solving problems. Vectors in 2 dimensional space and 3-dimensional space should be considered as starting examples of many theo-rems and problems. They will let you "see" what is happening. We have tried to give examples for each theorem and proposition. We would like to express our deepest gratitude to those mathematicians who o ered valuable suggestions leading to this textbook's improvements. Also we appreciate the great assistance of Kyung-Moon's sta , particularly Mr. Moon-Kyu Park and Mr. Jong-Wean Kim. Still, this book may contain some errors or shortcomings. As the student's instruction is our purpose, we welcome the con-structive criticism from students and instructors' invaluable insights to better this text and the consequent education. Please let us know if you have any com-
ments or questions by emailing us at the following addresses: namk@uww.edu, chenx@uww.edu, wang@hanyang.ac.kr, kslee@knue.ac.kr. We will provide pdf les of the text to any instructor who request it for classroom use.
1 Matrices. 7
1.1 Preliminaries . 7
1.2 Matrices. 10
1.3 Properties of a Matrix . 21
1.4 Block Matrices . 29

2 System of Linear Equations . 41
2.1 Gauss and Gauss-Jordan Elimination Method. 41
2.2 Inverse Matrix  . 66
2.3 Elementary Matrix Multiplication  . 80
2.4 Column Operations . 89

3 Vector Spaces . 95
3.1 Vector Spaces . 95
3.2 Geometry of Vectors and its Applications  . 102
3.3 Subspaces . 108
3.4 Basis of a Vector Space . 114
3.5 Row and Column Spaces . 134

4 Linear Transformations and Matrices . 153
4.1 Linear Transformations . 153
4.2 Matrix Representation of a Linear Transformation .  165
4.3 Composition of Linear Transformations and Matrix Multiplications 174
4.4 Isomorphisms. 181
4.5 Change of Bases . 185
4.6 Dual Spaces  . 189

5 Determinants . 195
5.1 De nition of Determinant . 195
5.2 Properties of Determinant  . 208
5.3 Cramer's Rule .216
5.4 LU Decomposition and Determinant .  225

6 Inner Product .  243
6.1 Inner Product .243
6.2 Gram-Schmidt Theorem . 256
6.3 Inner Product and Matrices . 264
6.4 Lines and Planes .  269

7 Eigenvalues and their Applications . 279
7.1 Hamilton-Cayley Theorem . 279
7.2 Eigenvalues and their Applications .  289
7.3 Diagonalization of a Square Matrix . 305
7.4 Symmetric Matrices .  316
7.5 Quadratic Forms . 325

8 Jordan and Other Canonical Forms .  335
8.1 Quotient Spaces .  335
8.2 Minimal Polynomials and Linear Transformations .  34
8.3 Triangular Forms .  346
8.4 Jordan Canonical Forms .360

Bibliography .  397
수학사 [경문수학산책 04]
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