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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