Alien plots coming from proje ctions of highD surfaces onto 3D subspaces. Perpendicular complement of a subspace. Null spaces of matrices. Complex eigenvalues and eigenvectors. The matrix exponential for di agonalizable and non-diagonalizable matrices.
Eigenvalues reveal long term behavior of matrix exponentials and matrix powers.
This is the main theoretical lesson. Discussion of the spectral theorem and its proof. Given an arbitrary matrix , using the spectral theorem applied to to explain why every matrix has a singular value decompositio n. MGM.11 Function Spaces Functions as vectors. The dot p roduct of two functions.