Matrices Overview

WGSL supports matrices between \(2 \times 2\) and \(4 \times 4\) f32 elements.

Matrices are declared with the form matCxR<f32>, where C is the number of columns in the matrix, and R is the number of rows in the matrix.

Example Matrix Declarations

Type	Description
mat2x3<f32>	A matrix with two columns and three rows of f32.
mat4x2<f32>	A matrix with four columns and two rows of f32.

matCxR<T> can be thought of as C column vectors of vecR<T>.

WGSL also predeclares the alias matCxRf as an alias for matCxR<f32>.

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What is "Column-Major"?

In WGSL, matrices are column-major. This is a critical concept to understand when working with matrix elements and indexing:

• Column Vector Basis: A matrix is treated as a collection of column vectors side-by-side, rather than row vectors. For example, a mat3x3f consists of 3 columns, where each column is a vec3f.
• Left-to-Right Construction: When you initialize a matrix with values (or elements/vectors), you specify them column by column (left-to-right), rather than row by row.
• First Index is Column: If you index a matrix using my_matrix[i], it extracts the \(i\)-th column vector (0-based), not a row.
• Double Indexing is [column][row]: To access a specific scalar element, use my_matrix[col][row]. For instance, my_matrix[1][2] accesses the element at Column 1, Row 2.
• Memory Layout: In memory, the elements of the first column are stored sequentially, followed by the elements of the second column, and so on.

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Next Steps

Matrix operations and usage:

• Matrix Constructors: Initialization forms including zero-value, column-wise, and scalar-wise constructors.
• Matrix Multiplication: Linear algebra operations, including scalar, vector, and matrix multiplications.

/*
 * Copyright ©2026 Michael R. Bernstein. Licensed under Apache 2.0.
 * See root README.md for global project-wide upstream attributions.
 */

const my_matrix = mat3x3f(
  vec3f(1.0, 2.0, 3.0), // Column 0
  vec3f(4.0, 5.0, 6.0), // Column 1
  vec3f(7.0, 8.0, 9.0)  // Column 2
);

fn get_column_1() -> vec3f {
  return my_matrix[1]; // Resolves to Column 1: vec3f(4.0, 5.0, 6.0)
}

fn get_element_1_2() -> f32 {
  return my_matrix[1][2]; // Column 1, Row 2 (0-based) -> 6.0
}

const m2x2 = mat2x2f(1.0, 2.0, 3.0, 4.0);