## 1. Week 3

### 1.1. introduction to matrices

### 1.2. matrices in linear algebra:operating on vectors

1.2.1. how matrices transform space

1.2.2. types of matrix transformation

1.2.3. composition and combination of matrix transformations

1.2.4. using matrices to make transformations

### 1.3. matrix inverses

1.3.1. solving the apples and bananas problems:Gaussian elimination

1.3.2. going from Gaussian elimination to finding the inverse matrix

1.3.3. solving the linear equations using the inverse matrix

### 1.4. special matrices and coding up some matrix operations

1.4.1. determinants and inverses

1.4.2. identifying special matrices

## 2. Week 4

### 2.1. matrices as objects that map one vector onto another;all the types of matrices

2.1.1. introduction Einstein summation convention and the symmetry of the dot product

2.1.2. non-square matrix multiplication

### 2.2. matrices transform into the new basis vectors set

2.2.1. matrices changing basis

2.2.2. doing a transformation in a changed basis

2.2.3. mapping to spaces with different numbers of dimensions

### 2.3. making multiple mappings,deciding id these are reversible

2.3.1. orthogonal matrices

### 2.4. recognizing mapping matrices and applying these to data

2.4.1. the Gram-Schmidt process

2.4.2. example:reflecting in a plane

2.4.3. reflecting Bear

## 3. Week 5

### 3.1. what are eigen-things?

3.1.1. what are eigenvalues and eigenvectors?

3.1.2. selecting eigenvectors by inspection

### 3.2. getting into the detail of eigenprolems

3.2.1. special eigen-cases

3.2.2. calculating eigenvectors

3.2.3. characteristic polynomials,eigenvalues and eigenvectors

### 3.3. when changing to the eigenbasis is really useful

3.3.1. changing to the eigenbasis

3.3.2. eigenbasis example

3.3.3. diagonalisation and applications

### 3.4. making the PageRank algorithm

## 4. Week 1

### 4.1. the relationship between machine learning,linear algebra and vectors and matrices.

### 4.2. vectors in data science

## 5. Wee 2

### 5.1. vectors

### 5.2. finding the size of a vector,its angle and projection.

### 5.3. changing the reference frame

5.3.1. changing basis

5.3.2. basis,vector space and linear independce

5.3.3. application of changing basis

5.3.4. doing some real-world vectors example