Matrix Operations and Determinants
1 hr 10 min 14 Examples
- Basic Algebraic Matrix Operations and Properties
- Performing Matrix Operations (Examples #1-8)
- Multiplying Two Matrices (Examples #9-10)
- Powers of a Matrix with Example
- Determinants: Overview and Calculation
- Calculating 2×2 Determinants (Examples #11-12)
- Calculating 3×3 Determinants (Examples #13-14)
- Theorem and Properties of Transpose Matrix Operations
Inverse Matrix
59 min 11 Examples
- Invertible Matrix: Overview and Definition
- Calculating Inverse: Theorem, Formula, and Examples (Examples #1-3)
- Algorithm for Finding Inverse Matrices: Overview
- Finding the Inverse of 2×2 and 3×3 Matrices (Examples #4-5)
- Solving System of Linear Equations Using Inverses: Overview and Proof
- Using Inverse to Solve Specific Matrix and Systems (Examples #6-8)
- Elementary Matrices: Facts, Definitions, and Inverses (Examples #9-11)
Invertible Matrix Theorem
34 min 10 Examples
- Inverse Matrices: Facts and Examples
- Find Matrix A Using Inverses (Example)
- Invertible Matrix Theorem and Related Questions (Five True/False Questions)
- Using Invertible Matrix Theorem with Implications (Three Examples)
- Determining Invertibility Quickly (Four Examples)
- Invertible Linear Transformations for Invertible Matrices
Partitioned Matrices
51 min 8 Examples
- Partitioned Matrix: Definition, Subdivisions, and Dimensions (Examples #1-2)
- Adding and Multiplying Partitioned Matrices: Overview and Example #3
- Column-Row Expansion of AB: Theorem
- Comfortably Partitioned Block Multiplication (Examples #4-6)
- Solving Partitioned Matrix Equations (Examples #7-8)
- Block Diagonal Matrices and Inverses of Partitioned Matrices: Overview
Matrix Factorization
1 hr 7 min 5 Examples
- LU-Factorization: Applications and Steps
- Finding LU-Factorization (Examples #1-3, Methods 1 and 2)
- Solving System of Linear Equations Using LU-Decomposition: Steps
- Solving Matrix Equations Using LU Factorization (Examples #4-5)
Applications to Computer Graphics
52 min 6 Examples
- Computer Graphics Applications: Overview and Basic Transformations
- Homogeneous Coordinates: Introduction and Composite Transformation Algorithm
- Composite 2D Transformations and Homogeneous Coordinates (Examples #1-5)
- Homogeneous 3D Coordinates and Perspective Projections Matrix
- Perspective Projection: Finding the Image (Example #6)
Chapter Test
1 hr 16 min 9 Problems
- Partitioned Matrix Calculations (Problem #1)
- Matrix Expression Definition (Problem #2a-e)
- Matrix Calculations: 3A – 2B (Problem #3)
- Finding Matrix A (Problem #4)
- Solving System Using Inverse and Algorithm (Problem #5)
- Partitioned Matrix Inverse Calculations (Problem #6)
- 3×3 Matrix Transformation (Problem #7)
- Solving Ax=b with LU Factorization (Problem #8)
- True or False (Problem #9a-e)