Math 316U - Spring Semester 2005 - Lectures

Questions regarding the lectures below can be sent to Prof. Williams by e-mail.

These notes will form the basis for part of the lectures. The remainder of each lecture period will be devoted to answering students' questions and solving problems.

• Lecture 1 (1/10/05) - Introduction to Systems of Linear Equations, Geometric Interpretations, and Review of Vectors

• Lecture 2 (1/12/05) - Matrices, Gauss-Jordan Elimination, and Reduced Row-Echelon Form

• Lecture 3 (1/19/05) - Solutions to Systems of Equations

• Lecture 4 (1/24/05) - Infinite Number of Solutions, Matrix-Matrix Multiplication, and Matrix Algebra

• Lecture 5 (1/26/05) - Linear Combinations, Linear Independence, and Span

• Lecture 6 (1/31/05) - Basis, Dimension, and Coordinates

• Lecture 7 (2/16/05) - Linear Transformations

• Lecture 8 (2/23/05) - Inverse of a Linear Transformation

• Lecture 9 (2/28/05) - Image and Kernel of a Linear Transformation

• Lecture 10 (3/14/05) - Change of Basis of a Linear Transformation

• Lecture 11 (4/4/05) - Gram-Schmidt Process and QR Factorization (in-class notes)

• Lecture 12 (4/6/05) - Determinants

• Lecture 13 (4/11/05) - Eigenvalues and Eigenvectors

• Lecture 14 (4/13/05) - Eigenbasis, Diagonalization, and Powers of a Matrix

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