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In this course, you will :
- Understanding Matrix Algebra and using it to solve linear equations and transformations, with Python examples.
- Vectors, vector properties, vector spaces, sub spaces, and application in coordinate systems are all covered. The fundamental subspaces and how to compute them
- Understanding of orthogonal and orthonormal vectors, as well as orthogonal projections. The minimal distances and Gram Schmidt orthogonalization are then computed.
- Matrix Eigen, cholesky, and singular value decompositions are examples of decompositions. Diagonalization, full rank approximation, and low rank approximation mastery
- Inverse matrix, least squares, and normal equation Linear Regression and House Prediction Practice on Kaggle
- Explaining and deducing Principal Component Analysis (PCA) and applying it to face recognition using the Eigen Faces algorithm from the ground up.
Syllabus :
1. Matrix Algebra
- Matrix Addition
- Matrix Multiplication
- Matrix Properties
- Matrix Transpose
- Matrix Inverse - Introduction
- Matrix Inverse - Echelon Rules
- Matrix Inverse - RREF
- Matrix Inverse - GAUSS
- Matrix Inverse - Computation
2. Systems of Linear Equations and Transformations
- Application of Matrix Inverse
- Gaussian Elimination
- Linear Transformations
- Transformation Matrix
- Special Matrix Transformations
3. Vectors
- Definition
- Addition and Multiplication of Vectors
- Dot Product
- Magnitude of a vector and unit vectors
- Distance between two vectors
4. Vector Algebra
- Subspaces
- Linear Combination
- Span
- Generated Subspace
- Linear Independence
- Fundamental Subspaces - Nul Spac
- Fundamental Subspaces - Column Space
- Basis
- Coordinate Systems and Change of Basis
- Dimension and Rank
5. Metric SPaces, Norm SPaces and Inner Product SPaces
- Metric and Normed Spaces
- Inner Product Spaces
6. Orthogonality
- Orthogonal and Orthonormal vectors
- Orthogonal Projection on 1-D Space
- Orthogonal Projection on N-D Space
- Minimal Distance
- Gram Schmidt
7. Determinant and Trace Operator
- Determinant Properties
- System of Linear Equations
- Inverse
- Areas and Volumes
- Trace
8 .Matrix Decomposition
- Eigen Decomposition
- Diagonalization
- Cholesky Decomposition
- Singular Value Decomposition
- Full rank approximation
- Low Rank Approximation
- Fundamental subspaces
9. Symmetric matrices and Quadratic form
- Symmetric matrices
- Quadratic forms
10. Matrix Inverses
- Left and Right Inverse
- Pseudo Inverse
11. Linear Regression Practice
- Least Square and Normal Equation
- Linear Regression
- Kaggle House Price Prediction
12. Face Recognition using PCA - Eigen Faces
- Pre-Requiscites and Rationale
- Principal Component Analysis Theory
- Eigen Faces
13. Appendix (Python Installation and Introduction)
- Python Installation
- Python Introduction
- Conditional Statements
- Loops
- Methods
