| # Vectors
| A vector is a collection of numbers arranged in a column or a row, and can be thought of as point in space. We review basic notion such as independence, span, subspaces, and dimension. The scalar product allows to define the length of a vector, as well as generalize the notion of angle between two vectors. Via the scalar product, we can view a vector as a linear function. We can also compute the projection of a vector onto a line defined by another — a basic ingredient in many visualization techniques for high-dimensional data sets.
Outline Basics Scalar product, norms and angles Projection on a line Orthogonalization Hyperplanes and half-spaces Linear functions Application: data visualization via projection on a line Exercises