Linear Algebra: Fundamentals Of Matrix Algebra

Learn the fundamentals you will need to understand advanced linear algebra concepts.

What you'll learn

Learn how to compute various properties of matrices & vectors.

Learn how to solve a system of linear equations using 3 different methods.

Learn how certain matrix operations apply to the real-world.

Develop a strong mathematical foundation for working with data.

Requirements

High-School Algebra

Description

Linear Algebra: Fundamentals of Matrix Algebra is designed to help you understand the fundamentals of Linear Algebra that will prepare you for more advanced courses in linear algebra. You will learn how to perform a lot of matrix computations from scratch, which will be essential when learning more abstract concepts as well as applying these techniques to real-world datasets.Topics covered include:Vector Operations: Lengths, Normalization, Dot Products, Angles, Cross Products.Matrix Operations & Types: Multiplication, Inversion, Reduced Row-Echelon FormSystems of Equations: Gaussian Elimination, LU Decomposition, Cramers RuleThis course is intended for anyone that is currently taking a linear algebra course, pursuing a data science career, or any other career that uses linear algebra concepts.This course will be followed up with a series on Linear Transformations & Vector Spaces, along with a course covering real-world applications. This is a pre-requisite to those courses and it is highly recommended that you complete this one first before moving on to the more advanced topics.Ingenium Academy is an online learning platform aimed at providing best-in-class coverage of all math & science-related subjects. We pride ourselves on our breadth and depth of coverage of subjects and aim to fulfill this by continuing to produce more courses.

Overview

Section 1: Vectors

Lecture 1 What Is A Vector?

Lecture 2 Adding Vectors

Lecture 3 Scalar Multiplication

Lecture 4 Calculating The Length of A Vector

Lecture 5 Dot Product

Lecture 6 Dot Product & Scalar Projections

Lecture 7 Calculating Angle Between Two Vectors

Lecture 8 Vector Normalization

Section 2: Matrices

Lecture 9 Introducing Matrices

Lecture 10 Matrix Addition

Lecture 11 Matrix Multiplication

Lecture 12 Properties of Matrix Multiplication

Lecture 13 Matrix Transpose

Lecture 14 Determinant of a Matrix

Lecture 15 Inverse of A 2x2 Matrix

Lecture 16 Inverse of A 3x3 Matrix

Lecture 17 The Outer Product

Lecture 18 Inner Product Definition

Lecture 19 Inner Product - Concrete Example

Lecture 20 Inner Product - Length of A Vector

Lecture 21 Inner Product - Distance Between Vectors

Lecture 22 Inner Product - Angle Between Vectors

Lecture 23 Types of Matrices

Lecture 24 Introduction to Orthogonal Matrices

Lecture 25 Orthogonal Matrices: Concrete Example - Part 1

Lecture 26 Orthogonal Matrices: Concrete Example - Part 2

Lecture 27 Permutation Matrices

Lecture 28 Gram Schmidt Process: Introduction

Lecture 29 Gram Schmidt Process: Concrete Example

Section 3: Systems of Linear Equations

Lecture 30 What Is A System of Linear Equations?

Lecture 31 Gaussian Elimination: Solving A System of Linear Equations

Lecture 32 LU Decomposition: Building Motivation

Lecture 33 LU Decomposition: Finding U

Lecture 34 LU Decomposition: Finding L

Lecture 35 LU Decomposition: Checking our Work

Lecture 36 Why Solving LUx=b is faster

Lecture 37 Cramers Rule: An Introduction

Lecture 38 Cramers Rule: A Concrete Example

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