Linear Algebra and Geometry 3

Linear Algebra and Geometry 3Inner product spaces, quadratic forms, and more advanced problem solvingChapter 1: Eigendecomposition, spectral decompositionS1. Introduction to the courseS2. Geometrical operators in the plane and in the 3-spaceYou will learn: using eigenvalues and eigenvectors of geometrical operators such as symmetries, projections, and rotations in order to get their standard matrices; you will also strengthen your understanding of geometrical transformations.

S3. More problem solving; spaces different from R^nYou will learn: work with eigendecomposition of matrices for linear operators on various vector spaces. S4.

Intermezzo: isomorphic vector spacesYou will learn: about certain similarities between different spaces and how to measure them. S5. Recurrence relations, dynamical systems, Markov matricesYou will learn: more exciting applications of eigenvalues and diagonalization.

S6. Solving systems of linear ODE, and solving higher order ODEYou will learn: solve systems of linear ODE and linear ODE of higher order with help of diagonalization. Chapter 2: Inner product spacesS7.