Math notes
This part of the site is a loose collection of my math notes.
- Angle between two vectors
- atan2
- Integrating sin² x
- Integrating cos² x
- Ray vs. sphere intersection
- Possible rotational symmetries in a Bravais lattice
1. Notation
Since there are so many conventions in linear algebra, I’ve decided to pick one and be consistent. Below is what I use throughout the site.
1.1. Vectors
| A vector (bold font). | |
| The norm of the vector (a scalar), if it appears in the text. Otherwise, it’s some scalar. | |
| The inner product of a vector with itself (a scalar). Equivalently, the norm of the vector squared. | |
| The norm of a vector expression (a scalar). | |
| The inner product of two vectors (a scalar). | |
| The cross product of two vectors (a vector). |
1.2. Matrices
| A matrix. | |
| A matrix product (a matrix). The former is premultiplying the latter or, equivalently, the latter is postmultiplying the former. | |
| A matrix premultiplying a vector or, equivalently, operating on it (a vector). | |
| The Kronecker product of two matrices (a matrix). | |
| The inverse of an invertible square matrix (a matrix). | |
| The determinant of a square matrix (a scalar). | |
| The trace of a square matrix (a scalar). |