Class Log
Numbers refer to sections of the textbook (Bretscher, Linear algebra with applications).
Thursday 4/30/15: 7.4 continued. Review of chapter 7.
Wednesday 4/29/15: 7.1,7.4: Examples of discrete dynamical systems.
Monday 4/27/15: 7.1,7.4: Computing powers of a matrix via diagonalization. Discrete dynamical systems.
Friday 4/24/15: 3 x 3 examples of eigenvalues, eigenvectors, and diagonalization.
Wednesday 4/22/15: 7.2,7.3: Algebraic and geometric multiplicity of eigenvalues. Eigenspaces. Examples.
Monday 4/20/15: No class (Patriots' day).
Friday 4/17/15: 7.2,7.3: The characteristic equation of an n x n matrix A is a polynomial equation of degree n, so it has at most n real solutions. If it has exactly n solutions then A is diagonalizable.
Wednesday 4/15/15: 7.2,7.3: The eigenvalues of an n x n matrix A are the solutions of the characteristic equation det(A-λI)=0. The eigenvectors for a given eigenvalue λ are obtained by solving the equation (A-λI)x=0 for x in Rn. Examples in the 2 x 2 case.
Monday 4/13/15: 7.1 Eigenvalues and eigenvectors. An n x n matrix A is diagonalizable if there is a basis of Rn consisting of eigenvectors of A.
Friday 4/10/15: 6.2: Multiplicative property determinants: det(AB)=det(A)det(B). Laplace expansion of a determinant along a row or column.
Wednesday 4/8/15: 6.1,6.2: Formula for n x n determinant. Computation of determinants using Gaussian elimination algorithm.
Monday 4/6/15: 6.1 Introduction to determinants. Geometric interpretation of determinants (6.3).
Friday 4/3/15: 4.3 continued.
Wednesday 4/1/15: 4.3 The matrix of a linear transformation.
Monday 3/30/15: 4.2 continued.
Friday 3/27/15: 4.2 Linear transformations of linear spaces.
Wednesday 3/25/15: 4.1 continued.
Monday 3/23/15: 4.1 Linear spaces (also known as vector spaces).
Friday 3/13/15: 3.4 continued.
Wednesday 3/11/15: 3.4 continued. Quiz 1
Monday 3/9/15: 3.4 Coordinates.
Friday 3/6/15: 3.3 continued.
Wednesday 3/4/15: 3.3 Dimension of a subspace, finding bases of the kernel and image of a linear transformation.
Monday 3/2/15: 3.2 continued.
Friday 2/27/15: 3.2 Subspaces of Rn, linear independence, and bases.
Tuesday 2/25/15: 3.1 continued.
Monday 2/23/15: 3.1 Image and kernel of a linear transformation.
Friday 2/20/15: 2.4 continued.
Wednesday 2/18/15: 2.4 Inverse of a linear transformation.
Monday 2/16/15: 2.3 Matrix products.
Friday 2/13/15: 2.2 Geometric examples of linear transformations.
Wednesday 2/11/15: 2.1 Linear transformations (continued).
Monday 2/9/15: Snow day
Friday 2/6/15: 2.1 Linear transformations.
Wednesday 2/4/15: 1.3 Matrix form of system of linear equations.
Monday 2/2/15: Snow day
Friday 1/30/15: 1.2 continued
Wednesday 1/28/15: Snow day
Monday 1/26/15: 1.2 Gaussian elimination algorithm for finding all solutions of systems of linear equations.
Friday 1/23/15: 1.1 (continued), see also 1.3. Number of solutions: a system of m linear equations in n variables has either 0,1 or infinitely many solutions. Typically we expect 0 for m > n, 1 for m=n, and infinitely many for m < n.
Wednesday 1/21/15: 1.1 Solving systems of linear equations. Geometric interpretation.