Matrices

Creating Matrices

use algebraeon::structures::Integer;
use algebraeon::rings::matrix::Matrix;

let a = Matrix::<Integer>::from_rows(vec![
    vec![1, 2, 3],
    vec![0, -1, 4],
]);

assert_eq!(a.rows(), 2);
assert_eq!(a.cols(), 3);

let zero = Matrix::<Integer>::zero(2, 3);
let ident = Matrix::<Integer>::ident(3);
let diag = Matrix::<Integer>::diag(&vec![1, 5, 9]);

assert_eq!(zero.rows(), 2);
assert_eq!(ident.cols(), 3);
assert_eq!(
    diag.get_row(0),
    vec![Integer::from(1), Integer::from(0), Integer::from(0)]
);

Basic Arithmetic

use algebraeon::structures::Integer;
use algebraeon::rings::matrix::Matrix;

let a = Matrix::<Integer>::from_rows(vec![
    vec![1, 2, 3],
    vec![0, 1, 4],
]);
let b = Matrix::<Integer>::from_rows(vec![
    vec![1, 0],
    vec![0, 1],
    vec![2, 3],
]);

let sum = Matrix::add(&a, &a).unwrap();
let product = Matrix::mul(&a, &b).unwrap();

assert_eq!(
    sum.get_row(0),
    vec![Integer::from(2), Integer::from(4), Integer::from(6)]
);
assert_eq!(
    product.get_row(0),
    vec![Integer::from(7), Integer::from(11)]
);
assert_eq!(
    product.get_row(1),
    vec![Integer::from(8), Integer::from(13)]
);

let scaled = a.clone().mul_scalar(&Integer::from(3));
let transposed = b.clone().transpose();

assert_eq!(
    scaled.get_row(1),
    vec![Integer::from(0), Integer::from(3), Integer::from(12)]
);
assert_eq!(
    transposed.get_row(0),
    vec![Integer::from(1), Integer::from(0), Integer::from(2)]
);

use algebraeon::structures::Integer;
use algebraeon::rings::matrix::Matrix;
let v = Matrix::<Integer>::from_rows(vec![vec![1, 2, 3]]);
let w = Matrix::<Integer>::from_rows(vec![vec![4, 5, 6]]);
assert_eq!(Matrix::dot(&v, &w), Integer::from(32));

Determinants, Rank, and Inverses

use algebraeon::structures::{Integer, Rational};
use algebraeon::rings::matrix::Matrix;

let integer_matrix = Matrix::<Integer>::from_rows(vec![
    vec![1, 2],
    vec![3, 5],
]);
assert_eq!(
    integer_matrix.clone().det().unwrap(),
    Integer::from(-1)
);
assert_eq!(integer_matrix.rank(), 2);

let rational_matrix = Matrix::<Rational>::from_rows(vec![
    vec![2, 4, 4],
    vec![-6, 6, 12],
    vec![10, 7, 17],
]);
let inverse = Matrix::inv(&rational_matrix).unwrap();
assert_eq!(Matrix::mul(&rational_matrix, &inverse).unwrap(), Matrix::ident(3));