Matrices, vectors, addition, scalar multiplication, matrix vector multiplication, matrix matrix multiplication, properties of matrix multiplication, inverse matrix and transposing matrices.

## 1. Matrices and Vectors

I would like to give full credits to the respective authors as these are my personal python notebooks taken from deep learning courses from Andrew Ng, Data School and Udemy :) This is a simple python notebook hosted generously through Github Pages that is on my main personal notes repository on https://github.com/ritchieng/ritchieng.github.io. They are meant for my personal review but I have open-source my repository of personal notes as a lot of people found it useful.

### 1a. Matrices

- Rectangular array of numbers
- 2D array
- Number of
**Rows**x Number of**Columns**

### 1b. Vector

- n x 1 matrix
- y(i): i-th element
- 1-indexed (start from 1-th)
- Normally this

- 0-indexed (start from 0-th)
- Used in Machine Learning

## 2. Addition and Scalar Multiplication

### 2a. Addition

- You can only add matrices with the same dimensions (r x c)

### 2b. Scalar (Number) Multiplication

- Example

## 3. Matrix Vector Multiplication

- Example
- Theory
- Application to hypothesis by converting given data to matrix
- prediction = data_matrix x parameters

## 4. Matrix Matrix Multiplication

- Example
- Theory
- Application to hypothesis by converting given data to matrix
- There are linear algebra libraries to do these calculations

## 5. Properties of Matrix Multiplication

- Not commutative
- Associative
- A x B x C = (A x B) x C = A x (B x C)

- Identity Matrix

## 6. Inverse and Transpose

### 6a. Inverse

- A * A_inverse = Identity Matrix
- A_inverse = pinv(A)
- You can use octave code pinv(A)

- Matrices without inverse –> singular or degenerate

### 6b. Transpose

- Example and theory