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In this course, you will :
- Learning the complex concepts of linear algebra from the ground up.
- Python is used to demonstrate working knowledge of various linear algebra techniques.
- Animated explanations of concepts such as vector space, spans, and subspace.
- Knowledge of important concepts such as fields, eigenspaces, diagonalization, and SVD.
- An understanding of how linear algebra concepts are used to construct the most useful data science tools, such as neural networks.
- Through coding exercises and practical projects, you will be able to apply linear algebra concepts to real-world problems.
Syllabus :
1. Linearity
- Functions in Data Science
- Linear Functions
- Linear Combinations
- Convex Combinations
- Linear Independence
- Linear Systems
2. Matrices
- Matrices
- Matrix Multiplication
- Matrix Operations
3. Solving Linear Systems
- Solution Preserving Operations
- Echelon Matrices
- Gaussian Elimination
- Gaussian Elimination Using Python
- Solution Set of a Linear System
- Geometric Interpretation of Inconsistency
- Verifying Linear Independence
- Rank of a Matrix
- Challenge: Check Linear Independence
- Solution Set and Rank
4. Singularity
- Elementary MatricesInverse of a Square Matrix
- Determinant of a Matrix
- Determinant by Pivots: A Python AlgorithmInverse of a Rectangular Matrix
5. Linear Regression and Least Squares
- Approximate Solution
- Least Squared Error Solution
- Linear Regression on Real Dataset
- Multi-target Linear Regression
- Polynomial Regression
- Non-linear Regression
- Classification Through Regression
- Neural Networks
6. Vector Space
- Vector Generalization
- Set and Closure Property
- Group and Field
- Finite Field
- Vector Space
- Finite Vector Space
- Span, Basis, and Dimensions
- Subspace
- Dot Product vs. Inner Product
- Vector Space in Data Science
7. Vector Spaces of a Matrix
- Column Space
- Row Space and Null Space
- Orthogonal Spaces and Complements
- Eigenspace
8. Singular Value Decomposition: SVD
- Orthogonal Diagonalization
- Singular Value Decomposition: SVD
