Copies of the classnotes are on the internet in PDF and Postscript formats as given below.

Chapter 1: Vectors, Matrices, and Linear Systems.

• Section 1-1: Vectors in Euclidean Spaces. PDF. PS.
• Section 1-2: The Norm and Dot Product. PDF. PS.
• Section 1-3: Matrices and Their Algebra. PDF. PS.
• Section 1-4: Solving Systems of Linear Equations. PDF. PS.
• Section 1-5: Inverses of Square Matrices. PDF. PS.
• Section 1-6: Homogeneous Systems, Subspaces, and Bases. PDF. PS.

Chapter 2: Dimension, Rank, and Linear Transformations.

• Section 2-1: Independence and Dimension. PDF. PS.
• Section 2-2: The Rank of a Matrix. PDF. PS.
• Section 2-3: Linear Transformations of Euclidean Spaces. PDF. PS.
• Section 2-4: Linear Transformations of the Plane (in brief). PDF. PS.
• Section 2-5: Lines, Planes, and Other Flats. PDF. PS.

Chapter 3: Vector Spaces.

• Section 3-1: Vector Spaces. PDF. PS.
• Section 3-2: Basic Concepts of Vector Spaces. PDF. PS.
• Section 3-3: Coordinatization of Vectors. PDF. PS.
• Section 3-4: Linear Transformations. PDF. PS.
• Section 3-5: Inner-Product Spaces. PDF. PS.

Chapter 4: Determinants.

• Section 4-1: Areas, Volumes, and Cross Products. PDF. PS.
• Section 4-2: The Determinant of a Square Matrix. PDF. PS.
• Section 4-3: Computation of Determinants and Cramer's Rule. PDF. PS.

Chapter 5: Eigenvalues and Eigenvectors.

• Section 5-1: Eigenvalues and Eigenvectors. PDF. PS.
• Section 5-2: Diagonalization. PDF. PS.

Chapter 6: Orthogonality.

• Section 6-1: Projections. PDF. PS.
• Section 6-2: The Gram-Schmidt Process. PDF. PS.
• Section 6-3: Orthogonal Matrices. PDF. PS.

Chapter 7: Change of Basis.

• Section 7-1: Coordinatization and Change of Basis. PDF. PS.
• Section 7-2: Matrix Representations and Similarity. PDF. PS.

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