Beginner – Expert Linear Algebra, with Practice in Python.

Master Linear Algebra, with clear and concise explanations, Practical Examples in various domains like Machine Learning.

Language: english

Note: 4.0/5 (22 notes) 6,368 students

Instructor(s): Neuralearn Dot AI

Last update: 2021-12-02

What you’ll learn

Understanding Matrix Algebra and applying it in solving linear equations and transformations, with practical examples in Python.
Mastering vectors, vector properties, vector spaces, sub spaces and application in coordinate systems. Fundamental sub spaces and how they can be computed.
Mastery of Orthogonal and Orthonormal vectors and orthogonal projections. Then computing minimal distances & Gram Schmidt orthogonalization.
Matrix Decompositions like eigen, cholesky and singular value decompositions. Mastery of Diagonalization, full rank approximation and low rank approximation.
Matrix inverses, least square and normal equation. Linear Regression and Kaggle House Prediction Practice.
Explaining and deducing Principal Component Analysis (PCA) from scratch and applying it to face recognition using the Eigen Faces algorithm.

Requirements

Basic Algebra.
No programming Experience Needed.

Description

In this course, we look at core Linear Algebra concepts and how it can be used in solving real world problems. We shall go through core Linear Algebra topics like Matrices, Vectors and Vector Spaces. If you are interested in learning the mathematical concepts in linear algebra, but also want to apply those concepts to datascience, statistics, finance, engineering, etc.then this course is for you! We shall explain detaily all Maths Concepts and also implement them programmaticaly in Python. We lay much emphasis on feedback. Feel free to ask as many questions as possible!!! Let’s make this course as interactive as possible, so that we still gain that classroom experience.

Here are the different concepts you’ll master after completing this course.

Fundamentals of Linear Algebra
Operations on a single Matrix
Operations on two or more Matrices
Performing Elementary row operations
Finding Matrix Inverse
Gaussian Elimination Method
Vectors and Vector Spaces
Fundamental Subspaces
Matrix Decompositions
Matrix Determinant and the trace operator
Core Linear Algebra concepts used in Machine Learning and Datascience
Hands on experience with applying Linear Algebra concepts using the computer with the Python Programming Language
Apply Linear Algebra in real world problems
Skills needed to pass any Linear Algebra exam
Principal Component Analysis
Linear Regression

YOU’LL ALSO GET:

Lifetime access to This Course
Friendly and Prompt support in the Q&A section
Udemy Certificate of Completion available for download
30-day money back guarantee

Who this course is for:

Computer Vision practitioners who want to learn how state of art computer vision models are built and trained using deep learning.
Anyone who wants to master deep learning fundamentals and also practice deep learning using best practices in TensorFlow.
Deep Learning Practitioners who want gain a mastery of how things work under the hood.
Beginner Python Developers curious about Deep Learning.

Enjoy!!!

Who this course is for

Computer scientists, who want to gain a solid foundation in linear algebra and apply it in solving computer related problems
Data scientists and Machine Learning Practitioners or Learners, who want to gain a solid foundation in linear algebra and apply it in solving problems in data science and machine learning.
Mathematics students, who want to gain a solid foundation in linear algebra and apply it in their mathematics courses.
Finance experts, who want to gain a solid foundation in linear algebra and apply it in solving real world problems
Engineers and Engineering students, who want to gain a solid foundation in linear algebra and use it solving engineering related problems.

Course content

Welcome and Introduction
- Welcome
- General Introduction
- About this Course
- Important Information
Matrix Algebra
- Matrix Definition 1
- Matrix Definition 2
- Matrix Addition
- Matrix Multiplication 1
- Matrix Multiplication 2
- Matrix Properties
- Matrix Transpose
- Matrix Inverse – Introduction
- Matrix Inverse – Echelon Rules
- Matrix Inverse – RREF
- Matrix Inverse – GAUSS
- Matrix Inverse – Computation
- Practical Session
Systems of Linear Equations and Transformations
- Problem Statement
- Application of Matrix Inverse
- Gaussian Elimination
- Linear Transformations
- Transformation Matrix
- Special Matrix Transformations
- Practical Session
Vectors
- Definition
- Addition and Multiplication of Vectors
- Dot Product
- Magnitude of a vector and unit vectors
- Distance between two vectors
- Cross Product
Vector Algebra
- Definition
- Subspaces
- Linear Combination
- Span
- Generated Subspace
- Linear Independence
- Fundamental Subspaces – Nul Space
- Fundamental Subspaces – Column Space
- Basis
- Coordinate Systems and Change of Basis
- Dimension and Rank
- Practical Session
Metric SPaces, Norm SPaces and Inner Product SPaces
- Metric and Normed Spaces
- Inner Product Spaces
Orthogonality
- Orthogonal and Orthonormal vectors
- Orthogonal Projection on 1-D Space
- Orthogonal Projection on N-D Space
- Minimal Distance
- Gram Schmidt
- Practical Session
Determinant and Trace Operator
- Definition
- Determinant Properties
- System of Linear Equations
- Inverse
- Areas and Volumes
- Trace
- Practical Session
Matrix Decomposition
- Definition
- Eigen Decomposition
- Diagonalization
- Cholesky Decomposition
- Singular Value Decomposition
- Full rank approximation
- Low Rank Approximation
- Fundamental subspaces
- Practical Session
Symmetric matrices and Quadratic form
- Symmetric matrices
- Quadratic forms
Matrix Inverses
- Left and Right Inverse
- Pseudo Inverse
Linear Regression Practice
- Pre-Requiscites
- Least Square and Normal Equation
- Linear Regression
- Kaggle House Price Prediction
Face Recognition using PCA – Eigen Faces
- Pre-Requiscites and Rationale
- Principal Component Analysis Theory
- Eigen Faces
Appendix (Python Installation and Introduction)
- Python Installation
- Python Introduction
- Conditional Statements
- Loops
- Methods