// SPDX-License-Identifier: CC-BY-SA-4.0
// Copyright © Paweł Redman

#import "/common.typ": post, link-self

#show: post.with(
    title: "Math notes",
)

This part of the site is a loose collection of my math notes.

- #link-self("math/angle_between_two_vectors")[Angle between two vectors]
- #link-self("math/atan2")[atan2]
- #link-self("math/integrating_sin2x")[Integrating sin² x]
- #link-self("math/integrating_cos2x")[Integrating cos² x]
- #link-self("math/ray_vs_sphere")[Ray vs. sphere intersection]
- #link-self("math/rotational_symmetries_bravais_lattice")[Possible rotational symmetries in a Bravais lattice]

= 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.

== Vectors

#table(
    columns: 2,
    [$bold(x)$], [A vector (bold font).],
    [$x$], [The norm of the vector $bold(x)$ (a scalar), if it appears in the text. Otherwise, it's some scalar.],
    [$x^2$], [The inner product of a vector with itself (a scalar). Equivalently, the norm of the vector squared.],
    [$|bold(a) + bold(b) times bold(c)|$], [The norm of a vector expression (a scalar).],
    [$bold(a) dot bold(b)$], [The inner product of two vectors (a scalar).],
    [$bold(a) times bold(b)$], [The cross product of two vectors (a vector).],
)

== Matrices

#table(
    columns: 2,
    [$hat(M)$], [A matrix.],
    [$hat(A) hat(B)$], [A matrix product (a matrix). The former is *premultiplying* the latter or, equivalently, the latter is *postmultiplying* the former.],
    [$hat(M) bold(x)$], [A matrix premultiplying a vector or, equivalently, operating on it (a vector).],
    [$hat(A) times.circle hat(B)$], [The Kronecker product of two matrices (a matrix).],
    [$hat(M)^(-1)$], [The inverse of an invertible square matrix (a matrix).],
    [$op("det") hat(M)$], [The determinant of a square matrix (a scalar).],
    [$op("Tr") hat(M)$], [The trace of a square matrix (a scalar).],
)