Linear algebra

Linear algebra develops vectors and the maps between vector spaces. You begin with vector arithmetic and magnitude, then define vector spaces and the spaces of matrices and polynomials that behave the same way. The middle units build the dot product, orthogonality, and projections, and the later units turn to linear maps and the matrices that carry out dilation, rotation, reflection, shears, and their composition.

Each lesson sets an explanation next to guided proofs you assemble from blocks or complete a step at a time, with computation you enter directly, and about two thirds of the problems carry hints. All ten units of the outline are published; they are still slim, and lessons are being added within them.