ABSTRACT

This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finis

part 1|212 pages

Affine Geometry

chapter 1|10 pages

Vectors and vector spaces

chapter 2|12 pages

Matrices

chapter 3|18 pages

Systems of linear equations

chapter 4|22 pages

Some linear algebra

chapter 5|8 pages

Rank

chapter 6|20 pages

Determinants

chapter 7|13 pages

Affine space (I)

chapter 8|12 pages

Affine space (II)

chapter 9|12 pages

Geometry in affine planes

chapter 10|15 pages

Geometry in 3-dimensional affine space

chapter 11|18 pages

Linear maps

chapter 13|17 pages

Linear operators

chapter 14|17 pages

Transformation groups

part 2|114 pages

Euclidean Geometry

chapter 15|16 pages

Bilinear forms and quadratic forms

chapter 16|7 pages

Diagonalizing quadratic forms

chapter 17|16 pages

Scalar product

chapter 18|5 pages

Vector product

chapter 19|19 pages

Euclidean spaces

chapter 20|17 pages

Unitary operators and isometries

chapter 22|5 pages

Diagonalizing symmetric operators

chapter 23|11 pages

The complex case