1. Introduction to Vectors

1.4hr

1.1.1. Basics of Vectors5 min

1.1.2. Example1 min

1.1.3. Example1 min

1.1.4. Practice2 min

1.2.1. Vector Operations8 min

1.2.7. Practice (Tricky)5 min

1.3.1. Vector Properties4 min

1.3.2. Example3 min

1.3.3. Example3 min

1.3.4. Practice: Vector Properties2 min

1.4.1. Vector Norm5 min

1.5.1. Unit Vectors5 min

1.5.2. Example2 min

1.5.3. Practice2 min

1.6.1. Basics of Dot Product2 min

1.6.2. Example2 min

1.6.3. Practice1 min

1.7.1. Dot Product Properties3 min

2. Solving Linear Equations

1.8hr

2.1.1. Basics of Systems of Linear Equations8 min

2.1.2. Example3 min

2.1.3. Practice2 min

2.1.4. Practice3 min

2.2.1. Augmented Matrix3 min

2.3.1. Echelon Forms5 min

2.4.1. Reducing a Matrix5 min

2.5.1. Rank of a Matrix5 min

2.5.2. Example3 min

2.5.3. Practice38 sec

2.5.4. Practice1 min

2.6.1. Solving Linear Systems5 min

2.6.2. Homogeneous Systems2 min

2.7.1. Geometric Interpretation of Solutions to SLEs4 min

2.7.2. Example3 min

2.7.3. Practice3 min

2.8.1. Polynomial Interpolation5 min

2.8.2. Example4 min

2.8.3. Practice4 min

3. Matrices

1.5hr

3.1.1. Basics of Matrices3 min

3.1.2. Matrix Arithmetic3 min

3.1.3. Example1 min

3.1.4. Practice2 min

3.2.1. Matrix Multiplication6 min

3.3.1. Matrix Transpose3 min

3.3.2. Symmetric Matrices3 min

3.3.3. Example3 min

3.3.4. Practice60 sec

3.3.5. Practice2 min

3.4.1. Matrix Inverse4 min

3.4.2. Example3 min

3.4.3. Practice32 sec

3.4.4. Practice2 min

3.5.1. Matrix Inverse Algorithm3 min

3.5.2. Example2 min

3.5.3. Example2 min

3.5.4. Practice2 min

3.6.1. Elementary Matrices7 min

3.7.1. Invertible Matrix Theorem2 min

3.7.2. Example1 min

3.7.3. Practice1 min

3.8.1. Solving Matrix Equations2 min

3.8.2. Example52 sec

3.8.3. Example4 min

3.8.4. Practice2 min

3.8.5. Practice54 sec

3.8.6. Practice2 min

4. Vector Spaces and Subspaces

1.3hr

5. Orthogonality

33min

5.1.1. Projection and Perpendicular3 min

5.1.6. Practice: Projections

5.2.1. Orthonormal Set3 min

5.2.2. Example2 min

5.2.3. Gram-Schmidt Process3 min

5.2.4. Example4 min

5.2.5. Practice

5.3.1. Least Squares Approximation6 min

5.3.2. Example4 min

5.3.3. Example: Least Squares for Polynomials

5.3.4. Practice

6. Determinants

58min

7. Eigenvalues and Eigenvectors (Spectral Theory)

1.1hr

7.1.1. Eigenvalues and Eigenvectors6 min

7.1.2. Example7 min

7.1.3. Practice8 min

7.1.4. Practice4 min

7.2.1. Complex Eigenvalues

7.2.2. Example

7.2.3. Example

7.2.4. Practice

7.3.1. Properties of Eigenvectors and Eigenvalues3 min

7.3.2. Example3 min

7.3.3. Example6 min

7.3.4. Practice2 min

7.4.1. Diagonalization6 min

7.4.2. Example7 min

7.4.3. Practice2 min

7.4.4. Practice6 min

7.5.1. Symmetric Matrices3 min

7.5.2. Example: Symmetric Matrices4 min

8. Linear Transformations

49min

8.1.1. Linear Transformations6 min

8.2.1. Composition and Inverse3 min

8.2.2. Example4 min

8.2.3. Practice3 min

8.3.1. Special Linear Transformations in

\reals^2

MATH-1250

Course Overview

1. Introduction to Vectors

2. Solving Linear Equations

3. Matrices

4. Vector Spaces and Subspaces

5. Orthogonality

6. Determinants

7. Eigenvalues and Eigenvectors (Spectral Theory)

8. Linear Transformations

Midterm 2 Overview

Course Notes