Copies of the classnotes are on the internet in PDF format as given below. The "Examples, Exercises, and Proofs" files are PDF files prepared in Beamer and they contain worked examples and exercises (and a few proofs) which are not in the regular classnotes. The "Printout of Examples, Exercises, and Proofs" are printable PDF files of the Beamer slides condensed and without the pauses so that you can have a version that takes less paper to print than the regular "Examples, Exercises, and Proofs" files.

• Chapter 1. Vectors, Matrices, and Linear Systems.
• Chapter 2. Dimension, Rank, and Linear Transformations.
• Chapter 3. Vector Spaces.
• Chapter 4. Determinants.
• Chapter 5. Eigenvalues and Eigenvectors.
• Chapter 6. Orthogonality.
• Chapter 7. Change of Basis.
• Chapter 8. Eigenvalues: Further Applications and Computations.
• Chapter 9. Complex Scalars.
• Chapter 10. Solving Large Linear Systems.

Chapter 1: Vectors, Matrices, and Linear Systems.

• Section 1.1: Vectors in Euclidean Spaces. Section 1.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.1. Beamer file of Section 1.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.1. Print file of Section 1.1 proofs and examples
• Section 1.2: The Norm and Dot Product. Section 1.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.2. Beamer file of Section 1.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.2. Print file of Section 1.2 proofs and examples
• Section 1.3: Matrices and Their Algebra. Section 1.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.3. Beamer file of Section 1.3 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.3. Print file of Section 1.3 proofs and examples
• Section 1.4: Solving Systems of Linear Equations. Section 1.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.4. Beamer file of Section 1.4 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.4. Print file of Section 1.4 proofs and examples
• Section 1.5: Inverses of Square Matrices. Section 1.5 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.5. Beamer file of Section 1.5 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.5. Print file of Section 1.5 proofs and examples
• Section 1.6: Homogeneous Systems, Subspaces, and Bases. Section 1.6 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.6. Beamer file of Section 1.6 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.6. Print file of Section 1.6 proofs and examples
• Section 1.7: Application to Population Distributions. Section 1.7 notes
• Supplement. Examples, Exercises, and Proofs from Section 1.7. Beamer file of Section 1.7 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 1.7. Print file of Section 1.7 proofs and examples
• Section 1.8: Application to Binary Linear Codes.
• Study Guide 1

Chapter 2: Dimension, Rank, and Linear Transformations.

• Section 2.1: Independence and Dimension. Section 2.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.1. Beamer file of Section 2.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.1. Print file of Section 2.1 proofs and examples
• Section 2.2: The Rank of a Matrix. Section 2.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.2. Beamer file of Section 2.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.2. Print file of Section 2.2 proofs and examples
• Section 2.3: Linear Transformations of Euclidean Spaces. Section 2.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.3. Beamer file of Section 2.3 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.3. Print file of Section 2.3 proofs and examples
• Section 2.4: Linear Transformations of the Plane. Section 2.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.4. Beamer file of Section 2.4 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.4. Print file of Section 2.4 proofs and examples
• Section 2.5: Lines, Planes, and Other Flats. Section 2.5 notes
• Supplement. Examples, Exercises, and Proofs from Section 2.5. Beamer file of Section 2.5 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 2.5. Print file of Section 2.5 proofs and examples
• Study Guide 2

Chapter 3: Vector Spaces.

• Section 3.1: Vector Spaces. Section 3.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 3.1. Beamer file of Section 3.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.1. Print file of Section 3.1 proofs and examples
• Section 3.2: Basic Concepts of Vector Spaces. Section 3.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 3.2. Beamer file of Section 3.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.2. Print file of Section 3.2 proofs and examples
• Section 3.3: Coordinatization of Vectors. Section 3.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 3.3. Beamer file of Section 3.3 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.3. Print file of Section 3.3 proofs and examples
• Section 3.4: Linear Transformations. Section 3.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 3.4. Beamer file of Section 3.4 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.4. Print file of Section 3.4 proofs and examples
• Section 3.5: Inner-Product Spaces. Section 3.5 notes
• Supplement. Examples, Exercises, and Proofs from Section 3.5. Beamer file of Section 3.5 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 3.5. Print file of Section 3.5 proofs and examples
• Study Guide 3

Chapter 4: Determinants.

• Section 4.1: Areas, Volumes, and Cross Products. Section 4.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.1. Beamer file of Section 4.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.1. Print file of Section 4.1 proofs and examples
• Section 4.2: The Determinant of a Square Matrix. Section 4.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.2. Beamer file of Section 4.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.2. Print file of Section 4.2 proofs and examples
• Section 4.3: Computation of Determinants and Cramer's Rule. Section 4.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.3. Beamer file of Section 4.3 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.3. Print file of Section 4.3 proofs and examples
• Section 4.4: Linear Transformations and Determinants. Section 4.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 4.4. Beamer file of Section 4.4 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 4.4. Print file of Section 4.4 proofs and examples
• Study Guide 4

Chapter 5: Eigenvalues and Eigenvectors.

• Section 5.1: Eigenvalues and Eigenvectors. Section 5.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 5.1. Beamer file of Section 5.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 5.1. Print file of Section 5.1 proofs and examples
• Section 5.2: Diagonalization. Section 5.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 5.2. Beamer file of Section 5.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 5.2. Print file of Section 5.2 proofs and examples
• Section 5.3: Two Applications. Section 5.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 5.3. Beamer file of Section 5.3 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 5.3. Print file of Section 5.3 proofs and examples
• Study Guide 5

Chapter 6: Orthogonality.

• Section 6.1: Projections. Section 6.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 6.1. Beamer file of Section 6.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 6.1. Print file of Section 6.1 proofs and examples
• Section 6.2: The Gram-Schmidt Process. Section 6.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 6.2. Beamer file of Section 6.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 6.2. Print file of Section 6.2 proofs and examples
• Section 6.3: Orthogonal Matrices. Section 6.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 6.3. Beamer file of Section 6.3 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 6.3. Print file of Section 6.3 proofs and examples
• Section 6.4: The Projection Matrix. Section 6.4 notes
• Supplement. Examples, Exercises, and Proofs from Section 6.4. Beamer file of Section 6.4 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 6.4. Print file of Section 6.4 proofs and examples
• Section 6.5: The Method of Least Squares. Section 6.5 notes
• Supplement. Examples, Exercises, and Proofs from Section 6.5. Beamer file of Section 6.5 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 6.5. Print file of Section 6.5 proofs and examples
• Study Guide 6

Chapter 7: Change of Basis.

• Section 7.1: Coordinatization and Change of Basis. Section 7.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 7.1. Beamer file of Section 7.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 7.1. Print file of Section 7.1 proofs and examples
• Section 7.2: Matrix Representations and Similarity. Section 7.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 7.2. Beamer file of Section 7.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 7.2. Print file of Section 7.2 proofs and examples
• Study Guide 7

Chapter 8: Eigenvalues: Further Applications and Computations.

• Section 8.1: Diagonalization of Quadratic Forms. Section 8.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 8.1. Beamer file of Section 8.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 8.1. Print file of Section 8.1 proofs and examples
• Section 8.2: Applications to Geometry. Section 8.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 8.2. Beamer file of Section 8.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 8.2. Print file of Section 8.2 proofs and examples
• Section 8.3: Applications to Extrema.
• Section 8.4: Computing Eigenvalues and Eigenvectors.
• Study Guide 8.

Chapter 9: Complex Scalars.

• Section 9.1: Algebra of Complex Numbers. Section 9.1 notes
• Supplement. Examples, Exercises, and Proofs from Section 9.1. Beamer file of Section 9.1 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 9.1. Print file of Section 9.1 proofs and examples
• Section 9.2: Matrices and Vector Spaces with Complex Scalars. Section 9.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 9.2. Beamer file of Section 9.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 9.2. Print file of Section 9.2 proofs and examples
• Section 9.3: Eigenvalues and Diagonalization. Section 9.3 notes
• Supplement. Examples, Exercises, and Proofs from Section 9.3. Beamer file of Section 9.3 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 9.3. Print file of Section 9.3 proofs and examples
• Section 9.4: Jordan Canonical Form.
• Study Guide 9.

Chapter 10: Solving Large Linear Systems.

• Section 10.1: Considerations of Time.
• Section 10.2: The LU-Factorization. Section 10.2 notes
• Supplement. Examples, Exercises, and Proofs from Section 10.2. Beamer file of Section 10.2 proofs and examples .
• Supplement. Printout of Examples, Exercises, and Proofs from Section 10.2. Print file of Section 10.2 proofs and examples
• Section 10.3: Pivoting, Scaling, and Ill-Conditioned Matrices.
• Study Guide 10.

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