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All LessonsFree Lessons (12)

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

Linear Algebra for Data Science Using Python/

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Quiz: Diagonalization and SVD

Quiz: Diagonalization and SVD

Test your understanding of the concepts you’ve learned so far.

We'll cover the following...

Multiple-choice questions

1.

To diagonalize a matrix, we compute ________.

A.

row space

B.

column space

C.

eigen space

D.

null space

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