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Linear Algebra for Data Science Using Python
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Introduction
Course Objectives
Linearity
Functions
Functions in Data Science
Linear Functions
Linear Combinations
Quiz: Linear Functions and Combinations
Challenge: Linear Combination Checker
Convex Combinations
Linear Independence
Linear Systems
Quiz: Convex Combinations and Linear Independence
Challenge: Linear System Solver
Matrices
Matrices
Matrix Multiplication
Matrix Operations
Quiz: Matrices and Matrix Operations
Challenge: Matrix Multiplier
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
Quiz: Linear Systems
Challenge: Calculate the Largest Independent Subset
Singularity
Elementary Matrices
Inverse of a Square Matrix
Determinant of a Matrix
Determinant by Pivots: A Python Algorithm
Inverse of a Rectangular Matrix
Quiz: Elementary and Invertible Matrix
Challenge: Lower-upper Decomposition Algorithm
Linear Regression and Least Squares
Approximate Solution
Least Squared Error Solution
Challenge: Sum of Squared Error Calculator
Linear Regression
Linear Regression on Real Dataset
Multi-target Linear Regression
Polynomial Regression
Non-linear Regression
Classification Through Regression
Neural Networks
Quiz: Regression and Classification
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
Quiz: Vector Space, Span, and Basis
Challenge: Subspace Dimension Finder
Vector Spaces of a Matrix
Column Space
Row Space and Null Space
Orthogonal Spaces and Complements
Eigenspace
Quiz: Null Space and Orthogonal Space
Singular Value Decomposition: SVD
Orthogonal Diagonalization
Singular Value Decomposition: SVD
Quiz: Diagonalization and SVD
Mini Project
Learning to Find Discriminative Null Space for Face Recognition
Subspace
Learn the concept of subspace.
We'll cover the following
Subspace
Examples
Line through the origin
The xy plane
Plane through the origin
Hyperplane through the origin
Zero-dimensional subspace
The subspace hierarchy
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