本帖隐藏的内容

Linearity is the main assumption used in all fields of science.

It gives a first approximation to any problem under study and is widely
used in economics and other social sciences. One may wonder why we decided
to write a book in linear algebra despite the fact that there are many excellent
books such as [10, 11, 19, 27, 34]? Our reasons can be summarized as follows.
First, we try to fit the course to the needs of the students in economics and the
students in mathematics and informatics who would like to get more knowledge in
economics. Second, we constructed all expositions in the book in such a way to
help economics students to learn mathematics and the proof making in mathematics
in a convenient and simple manner. Third, since the hours given to this course
in economics departments are rather limited, we propose a slightly different way
of teaching this course. Namely, we do not try to give all proofs of all theorems
presented in the course. Those theorems which are not proved are illustrated via
figures and examples, and we illustrated all notions appealing to geometric intuition.
Those theorems which are proved are proved in a most accurate way as it is done for
the students in mathematics. The main notions are always supported with economic
examples. The book provides many exercises referring to pure mathematics and
economics.

目录

1 Some Basic Concepts ....................................................... 1

2 Vectors and Matrices ....................................................... 17

3 Square Matrices and Determinants ...................................... 49

4 Inverse Matrix .............................................................. 65

5 Systems of Linear Equations .............................................. 75

6 Linear Spaces ............................................................... 91

7 Euclidean Spaces ........................................................... 107

8 Linear Transformations.................................................... 123

9 Eigenvectors and Eigenvalues ............................................. 141

10 Linear Model of Production in a Classical Setting ..................... 165

11 Linear Programming ....................................................... 195