Math 340L (Matrices and Matrix Calculations), Fall 2010, Lectures

Lecture schedule

Broadly speaking the aim is to cover the first six chapters of the text.

In more detail, below is a tentative schedule of the material to be covered; it will likely be adjusted as the semester goes on. Links to lecture notes will appear here after the lectures are given (usually within a few hours.) The notes are a transcript of exactly what appeared on the screen during class, except that if errors are discovered I will correct them.

All section references refer to the course text, Linear Algebra and its Applications, 3rd edition, by David Lay.

• Lecture 1 (26 Aug): Welcome; Section 1.1 (Systems of Linear Equations); beginning of Section 1.2 (Row Reduction and Echelon Forms)
• Lecture 2 (31 Aug): end of Section 1.2 (Row Reduction and Echelon Forms); most of Section 1.3 (Vector Equations)
• Lecture 3 (02 Sep): finish Section 1.3 (Vector Equations); Section 1.4 (Matrix Equations); begin Section 1.5 (Solution Sets of Linear Systems)
• Lecture 4 (07 Sep): finish Section 1.5 (Solution Sets of Linear Systems); Section 1.7 (Linear Independence)
• Lecture 5 (09 Sep): Section 1.8 (Introduction to Linear Transformations); Section 1.9 (The Matrix of a Linear Transformation)
• Lecture 6 (14 Sep): a few more comments on Sections 1.8-1.9 (linear transformations); part of Section 1.10 (an application of linear transformations to difference equations); most of Section 2.1 (Matrix Operations)
• Lecture 7 (16 Sep): Section 2.2 (The Inverse of a Matrix); parts of Section 2.3 (Characterizations of Invertible Matrices)
• Lecture 8 (21 Sep): more on Sections 2.2-2.3; identifying invertible matrices; brief look at Section 2.4 (Partitioned Matrices)
• Lecture 9 (23 Sep): begin Chapter 3 (Determinants)
• Lecture 10 (28 Sep): review for first midterm exam (extended by campus lockdown!)
• 30 Sep: First midterm exam
• Lecture 11 (05 Oct): midterm after-action report, finish Chapter 3 (Determinants)
• Lecture 12 (07 Oct): Section 4.1 (Vector Spaces and Subspaces)
• Lecture 13 (12 Oct): Section 4.2 (Null Spaces, Column Spaces and Linear Transformations); begin Section 4.3 (Linearly Independent Sets)
• Lecture 14 (14 Oct): Section 4.3 (Linearly Independent Sets, Bases); Section 4.4 (Coordinate Systems)
• Lecture 15 (19 Oct): end of Section 4.4 (Coordinate Systems); Section 4.5 (The Dimension of a Vector Space)
• Lecture 16 (21 Oct): Section 4.6 (Rank); Section 4.7 (Change of Basis)
• Lecture 17 (26 Oct): Section 5.1 (Eigenvectors and Eigenvalues); Section 5.2 (The Characteristic Equation)
• Lecture 18 (28 Oct): more on Sections 5.1-5.2; Section 5.3 (Diagonalization)
• Lecture 19 (02 Nov): Review for second midterm exam (brief highlights only, due to technical difficulties during the lecture)
• 04 Nov: Second midterm exam
• Lecture 20 (09 Nov): midterm after-action report; applications of diagonalization to dynamical systems
• Lecture 21 (11 Nov): more on dynamical systems; beginning of complex eigenvectors
• Lecture 22 (16 Nov): finish Chapter 5 (Eigenvectors and Eigenvalues); begin Section 6.1 (Inner Product, Length, and Orthogonality)
• Lecture 23 (18 Nov): pictures of dynamical systems (1, 2, 3); finish Section 6.1 (Inner Product, Length, and Orthogonality); begin Section 6.2 (Orthogonal Sets)
• Lecture 24 (23 Nov): finish Section 6.2 (Orthogonal Sets); Section 6.3 (Orthogonal Projection); Section 6.5 (Least-Squares Solutions); very brief treatment of Section 6.4 (Gram-Schmidt Orthogonalization)
• 30 Nov-02 Dec (2 lectures): guest lectures by Prof. Ray Heitmann