Matrix math for PHP.

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1.0.0 2015-11-07 05:31 UTC


Build Status

Stand-alone Linear Algebra Library for PHP


composer require mcordingley/LinearAlgebra

Alternately, include this in your composer.json and then update:

"mcordingley/linearalgebra": "^1.0.0"

If Composer isn't an option for you, download linear-algebra.phar and include it in your project. PHP will autoload classes from inside the archive as needed.


Start with a use statement for the class:

use mcordingley\LinearAlgebra\Matrix;

Then, instantiate a new instance of the matrix class like so:

$matrix = new Matrix([
    [0, 1, 2],
    [3, 4, 5],
    [6, 7, 8]

You can also generate an identity matrix with the identity factory function:

$threeByThreeIdentityMatrix = Matrix::identity(3);

With the matrix instance, you can retrieve individual elements with get using the zero-based indices of the row and column that you want:

$element = $matrix->get($row, $column);

It's also possible to find out how large the matrix is with the rows and columns properties:

$rows = $matrix->rows;
$columns = $matrix->columns;

You can also add, subtract, and multiply the matrix with scalar values and other matrices. All operations return a new Matrix and do not modify the underlying matrix:

$addedScalar = $matrix->add(3);
$addedMatrix = $matrix->add($anotherMatrix);
$subtractedScalar = $matrix->subtract(2);
$subtractedMatrix = $matrix->subtract($anotherMatrix);
$multipliedByScalar = $matrix->multiply(4);
$multipliedByMatrix = $matrix->multiply($anotherMatrix);

Matrices can be compared with equals to see if they're equal:

if ($matrix1->equals($matrix2)) {
    // Equality for all!

In addition to these basic operations, the Matrix class offers other common matrix operations:


It's also possible to run a map over the matrix:

$squaredElements = $matrix->map(function($element, $row, $column, $matrix) {
    return $element * $element


  • 1.0.0

    • Switch to PSR-4 from PSR-0.
    • Take isSymmetric() public.
    • Rearrange source in Matrix.php to be more readable and PSR-compliant.
  • 0.9.1

    • Fix several bugs with the Cholesky decomposition and inverse.
  • 0.9.0

    • Bump version up to represent that this is close to it's final form.
    • Merged PR for faster inverse calculations
    • KISS Vector class good-bye.
    • Renamed eq to equals.
    • Removed set function, so instantiated objects are immutable.
  • 0.3.0

    • Added the identity factory function
    • Using Cholesky decomposition for faster matrix inversions for applicable matrices
    • Added eq function to test equality of matrices
    • Implemented the ArrayAccess interface
  • 0.2.0

    • Created the Vector type
    • \MCordingley namespace is now \mcordingley
    • Matrix functions that return a new Matrix now return a new instance of the called class
  • 0.1.0

    • Created the Matrix type
    • Scalar Addition
    • Scalar Subtraction
    • Scalar Multiplication
    • Matrix Addition
    • Matrix Subtraction
    • Matrix Multiplication
    • Inverse
    • Adjoint
    • Determinant
    • Trace
    • Transpose
    • Submatrix
    • Map