Elementary linear algebra : applications version / Howard Anton, Chris Rorres.

Contents

CHAPTER 1 SYSTEMS OF LINEAR EQUATIONS AND METRICS
1.1 introduction to systems of linear equations
1.2 Gaussian elimination
1.3 matrices and matrix operations. etc

CHAPTER 2 DETERMINANTS
2.1 the determinant function
2.2 Evaluating determinants by the Row equation
2.3 properties of the determinant function, etc

CHAPTER 3 VECTORS IN 2-SPACE AND 3-SPACE
3.1 introduction to vectors
3.2 norm of a vector: vector arithmetic
3.3 Dot product: projections, etc

CHAPTER 4 EUCLIDEAN VECTOR SPACES
4.1 Euclidean n-space
4.2 linear transformations from Rn to Rm
4.3 properties of linear transformations Rn to Rm, etc

CHAPTER 5 GENERAL VECTOR SPACES
5.1 real vector spaces
5.2 subspaces
5.3 linear independence, etc

CHAPTER 6 INNER PRODUCT SPACES
6.1 inner products
6.2 Angle and orthogonality in inner product spaces, etc

CHAPTER 7 EIGENVAUES, EIGNVECTORS
7.1 Eigenvalues and Eigenvectors
7.2 diagonalization
7.3 Orthogonal Diagonalization

CHAPTER 8 LINEAR TRANSFORMATIONS
8.1 General linear transformations
8.2 Kernal and Range
8.3 Inverse linear transformations, etc

CHAPTER 9 ADDITIONAL TOPICS
9.1 application to differential equations
9.2 Geometry of linear operations on R2
9.3 Least squares fitting to data, etc

CHAPTER 10 COMPLEX VECTOR SPACES
10.1 Complex numbers
10.2 Division of complex numbers
10.3 Polar form of a complex number, etc

CHAPTER 11 APPLICATION OF LINEAR ALGEBRA
11.1 constructing curves and surfaces through specified points
11.2 Electrical networks
11.3 geometric linear programming, etc

Includes index : p. 813 - 822