# Artificial Intelligence

## Linear Algebra

An AI expert cannot live without **Linear Algebra**:

- Linear algebra is a branch of
**Mathematics** - Linear algebra plays an important role in
**Statistics** - Linear algebra represents
**the Math of Data**

## Linear Graphic

**Linear** means straight. A **Linear Graph** is a **Straight Line**.

In general, a linear graph displays a **Linear Function**.

A **Function ** is special relationship where each input has an output.

A function is often written as **f(x)** where x is the input value:

x | y | y = x |
---|---|---|

1 | 1 | when x = 1, y = 1 |

2 | 2 | when x = 2, y = 2 |

3 | 3 | when x = 3, y = 3 |

4 | 4 | when x = 4, y = 4 |

5 | 5 | when x = 5, y = 5 |

Results from f(x) = 2x

x | y | y = 2x |
---|---|---|

1 | 2 | when x = 1, y = 2 |

2 | 4 | when x = 2, y = 4 |

3 | 6 | when x = 3, y = 6 |

4 | 8 | when x = 4, y = 8 |

5 | 10 | when x = 5, y = 10 |

## Linear Equations

A Linear Equation is an equation for a straight line:

- y = x
- y = x*2
- y = x*2 + 7
- y = ax + b
- 5x = 3y
- y/2 = 6

A Linear Equation can NOT contain exponents or square roots:

- y = x**2
- y = Math.sqrt(x)
- y = Math.sin(x)

## Linear Regression

A Linear regression tries to model the relationship between two variables by fitting a linear graph to data.

One variable (x) is considered to be data, and the other (y) is considered to be dependent.

For example, a Linear Regression can be a model to relate the price of houses to their size.

## Linear Least Squares

Linear algebra is used to solve Linear Equations.

Linear Least Squares (LLS) is a set of formulations for solving statistical problems involved in Linear Regression.

## Matrix Factorization

With AI, you need to know how to factorize a matrix.

Matrix factorization is a key tool in linear algebra, especially in Linear Least Squares.