Linear analytic geometry. Linear dependence and independence, subspaces, basis. Inner products. Matrix algebra. Applications of the above will also be discussed.

The spectrum of the canonical operator in the noncommutative 2-torus Tθ depending on the parameter θ ∈ [0,1] © Douglas Hofstadter's butterfly. Licensed under ...

Linear transformations. Linear operators, change of basis, inner product and the diagonalization problem. Quadratic forms. Convex sets and geometric programming, input/output models for an economy, ...