Hello and welcome back to my blog!

I’ve decided to do something a little different this time around; I’ve updated and bought together some old reference material that I wrote, added some interactive demos and expanded on the diagrams. I hope that the result will serve as an accessible introduction to vector mathematics for games programmers.

### Definitions

- Scalars are written in lower case: a, b, c
- Vectors are written in upper case: A, B, C
- Matrices are written in bold upper case:
**A, B, C** - |a| mean abs(a), the absolute value of scalar a
- ||A|| means magnitude, or length of the vector A
- Ā means vector A is unit length
- Matrices are in row-major order, which means the rows are left to right in the matrix
**M**^{T}means the transpose of**M**

### Reading order

This is designed to be read in the following order:

But of course you can just use it as reference material.

### Contents

**Vectors**

All

Magnitude of vector

Unit vector

Dot product

Projection

The Cross and Wedge Products

Perpendicular operator

**Rotation**

All

Rotating a vector from world space into object space

Rotating a vector from object space to world space

**Matrices**

All

Multiplying two matrices

Rotating a matrix from world space into object space

Rotating a matrix from object space into world space

Transform point from world space into object space

Transform point from object space into world space

Transformation matrices

Inverse of a matrix

Orthonormal matrix

Determinant of a matrix

Until next time, have fun!

Cheers, Paul.

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Bookmarked!

Great stuff – took me back to my a-levels. Bookmarked until I unshackle myself from L.O.B. or my kids grow up….

Great stuff. Thanks!

Great work. Keep it up.

Thank you very much sir!!..

very cool of you. Keep it up!

thanks a lot!!!!

Good article. Keep it up!