# Linear Algebra

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Linear Algebra

## 2. Wee 2

### 2.3. changing the reference frame

2.3.1. changing basis

2.3.2. basis,vector space and linear independce

2.3.3. application of changing basis

2.3.4. doing some real-world vectors example

## 3. Week 3

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

3.2.1. how matrices transform space

3.2.2. types of matrix transformation

3.2.3. composition and combination of matrix transformations

3.2.4. using matrices to make transformations

### 3.3. matrix inverses

3.3.1. solving the apples and bananas problems:Gaussian elimination

3.3.2. going from Gaussian elimination to finding the inverse matrix

3.3.3. solving the linear equations using the inverse matrix

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

3.4.1. determinants and inverses

3.4.2. identifying special matrices

## 4. Week 4

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

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

4.1.2. non-square matrix multiplication

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

4.2.1. matrices changing basis

4.2.2. doing a transformation in a changed basis

4.2.3. mapping to spaces with different numbers of dimensions

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

4.3.1. orthogonal matrices

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

4.4.1. the Gram-Schmidt process

4.4.2. example:reflecting in a plane

4.4.3. reflecting Bear

## 5. Week 5

### 5.1. what are eigen-things?

5.1.1. what are eigenvalues and eigenvectors?

5.1.2. selecting eigenvectors by inspection

### 5.2. getting into the detail of eigenprolems

5.2.1. special eigen-cases

5.2.2. calculating eigenvectors

5.2.3. characteristic polynomials,eigenvalues and eigenvectors

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

5.3.1. changing to the eigenbasis

5.3.2. eigenbasis example

5.3.3. diagonalisation and applications