We here introduce vectors and matrices and the notion of dot product and matrix multiplication. We notice that the dot product is invariant under coordinate rotations, define linear dependence, and describe polar coordinates and their generalizations to three dimensions.
3.2 Rotating Coordinates in an Euclidean Space
3.3 The Dot Product
3.4 Matrix Multiplication
3.5 Linear Dependence and Independence
3.6 Polar Coordinates
3.7 Cylindric and Spherical Coordinates
3.8 Digression on Length and Distance in Vector Spaces