Math 213: Elementary Linear Algebra

Fall Semester 2021

Class Notes

1.1 The Geometry and Algebra of Vectors

1.2 Length and Angle: The Dot Product

1.3 Lines and Planes

1.3 Summary Lines and Planes

2.1 Introduction to Systems of Linear Equations

2.2 Solving a System of Linear Equations

2.3 Spanning Sets and Linear Independence

3.1 Matrix Operations

3.2 Matrix Algebra

3.2 Matrix Algebra (Suplement)

3.3 The Inverse of a Matrix

3.5a Subspaces and Bases

3.5bc Dimension and Rank

3.6 Linear Transformation

4.1 Eigenvalues and Eigenvectors in R^2

4.2a Introduction to Determinants

4.2b Determinants

4.3 Eigenvalues and Eigenvectors in R^n

4.4 Similarity and Diagonalization

5.1 Orthogonal Sets and Basis. Orthogonal Matrices

5.2 Orthogonal Complements and Orthogonal Projections

5.3 The Gram-Schmidt Process and the QR Factorization

5.4 Orthogonal Diagonalization of Symmetric Matrices

7.4 Singular Value Decomposition

7.4b Photo Application of Singular Value Decomposition