In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets – like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works.

Since we’re aiming at data-driven applications, we’ll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you’ll write code blocks and encounter Jupyter notebooks in Python, but don’t worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before.

At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these

Topic covered:

Solving data science challenges with mathematics

Motivations for linear algebra

Getting a handle on vectors

Operations with vectors

Modulus & inner product

Cosine & dot product

Projection

Changing basis

Basis, vector space, and linear independence

Applications of changing basis

Matrices, vectors, and solving simultaneous equation problems

How matrices transform space

Types of matrix transformation

Composition or combination of matrix transformations

Solving the apples and bananas problem: Gaussian elimination

Going from Gaussian elimination to finding the inverse matrix

Determinants and inverses

Einstein summation convention and the symmetry

Matrices changing basis

Doing a transformation in a changed basis

Orthogonal matrices

The Gram–Schmidt process

Gram-Schmidt process

What are eigenvalues and eigenvectors?

Special eigen-cases

Calculating eigenvectors

Changing to the eigenbasis

Eigenbasis example

Introduction to PageRank

This course is created by Imperial College London

If you like this video and course explanation feel free to take the

complete course and get certificate from: https://www.coursera.org/specializations/mathematics-machine-learning

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