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**This post is being continuously updated.**Last update: 5th of February, 2019**

### Intuition

- Every time you do matrix multiplication, you could view it as a transformation, where movement of space is involved.

### Notation

Term | Notation (denotation, short explanation) |
---|---|

vector |
$\vec{v}$, denoted by small letters with arrow above |

scalar |
any real number, e.g. $2$, $1/3$ or $\pi$ |

matrix |
A, denoted by capital letters and equals a $m\times n$ matrix |

$m\times n$ | m rows (horizontal) times n coloumns (vertical) |

basis vectors |
$\hat{i}$, $\hat{j}$, $\hat{k}$ - denoted by letters i, j and k with a hat over |

mapping (transformation) |
$T: \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}$, transformation from m to n dimension |

determinant |
scalar, the area or volume of vectors |

cross product |
length, perpendicular to the plane of two vectors in 3D |

dot product |
scalar, where a vector lands on another vector |