Math 1341B, Introduction to Linear AlgebraFall 2003 Peter Selinger

### What we did in each class:

 Sept 4: Course intro and OAC review: complex numbers (Ch. 1.7) Sept 9: OAC review: polar form, dot + cross product (Ch. 1.1-4, 1.6) Sept 11: OAC review: equation of planes, lines, intersection, angles (Ch. 1.5) Sept 16: math notation (sets, functions) (Ch. 4.1) Sept 17: vector spaces (Ch. 4.2-3) Sept 23: subspace test (Ch. 4.5) Sept 25: linear combinations, span (Ch. 4.4, 4.6 up to top of p.124) Sept 30: systems of linear equations, Gaussian elimination, echelon form (Ch. 3.1-3 and 3.5-6) Oct 2: Review, row canonical form (parts of Ch. 3.7) Oct 7: span of an infinite set, row/column space, linear independence (Ch. 4.6-4.7) Oct 9: linear independence examples, basis (Ch. 4.8) Oct 14: properties of bases, examples (Ch. 4.8, 3.11 up to p.86) Oct 16: Matrix multiplication (Ch. 2.1-3, 2.5) Oct 21: Problem solving skills, rank, row canonical form (Ch. 4.9, 3.7) Oct 23: matrix form of linear systems Ax=b, null space of a matrix, linear functions, examples in R^2, matrix of a linear function F:R^2->R^2 (Ch. 3.9, 5.3) Oct 28: fast matrix multiplication, inverse of a matrix, postscript demo (Ch. 2.9) Oct 30: coordinates, matrix of a general linear function (Ch. 4.11, 6.1-2, 6.5) Nov 4: trace, determinant, change of basis, composition of linear functions (Ch. 2.7, 8.1-6, 6.3) Nov 6: review Nov 11: change of basis and matrix representation of a linear function (Ch. 6.3) Nov 13: eigenvectors, eigenvalues, diagonalization (Ch. 9.1, 9.4-5) Nov 18: characteristic polynomial, multiplicity of eigenvalues, examples (Ch. 9.5) Nov 20: eigenspaces, polynomials of matrices, Cayley-Hamilton theorem, solving B^2=-I and B^2=A, similar matrices (Ch. 9.2, 9.3) Nov 25: eigenvectors and diagonalization of real symmetric matrices (Ch. 9.6). Example: coupled oscillations. Nov 27: image and kernel of linear maps, determinants via minors and cofactors (Ch. 5.4, 8.7). Example: Fourier analysis.

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Peter Selinger / Department of Mathematics and Statistics / Dalhousie University
selinger@mathstat.dal.ca / PGP key