Numerinus.Algebra 1.0.1

Here's the improved README.md file, incorporating the new content while maintaining the existing structure and information:

Numerinus.Algebra ??

Linear algebra module for the Numerinus mathematical suite. Built on top of Numerinus.Core, this package provides a fully generic Matrix<T> type that works with any numeric type implementing IArithmetic<T> � including Scalar, ComplexNumber, and any custom type you define.

Features

• Generic Matrix � Matrix<T> works with any IArithmetic<T> type.
• Operator Overloads � Use natural +, -, * syntax directly on matrices.
• Type-Safe Arithmetic � All cell-level math is delegated to T.Add, T.Multiply, etc.
• Dimension Validation � Built-in guards for incompatible matrix operations.

Project Structure

Numerinus.Algebra/ ??? Matrices/ ??? Matrix.cs ? Generic matrix type with arithmetic operators

Quick Start

Scalar Matrix

using Numerinus.Algebra.Matrices; using Numerinus.Core.Numerics;

// Create two 2x2 Scalar matrices var a = new Matrix<Scalar>(2, 2); a[0, 0] = 1; a[0, 1] = 2; a[1, 0] = 3; a[1, 1] = 4;

var b = new Matrix<Scalar>(2, 2); b[0, 0] = 5; b[0, 1] = 6; b[1, 0] = 7; b[1, 1] = 8;

var sum = a + b; // addition var diff = a - b; // subtraction var product = a * b; // multiplication

Console.WriteLine(product); // Matrix (2x2)

ComplexNumber Matrix

using Numerinus.Algebra.Matrices; using Numerinus.Core.Numerics;

var m = new Matrix<ComplexNumber>(2, 2); m[0, 0] = new ComplexNumber(1, 2); m[0, 1] = new ComplexNumber(3, 4); m[1, 0] = new ComplexNumber(5, 6); m[1, 1] = new ComplexNumber(7, 8);

var result = m * m; // multiplies using complex number arithmetic Console.WriteLine(result); // Matrix (2x2)

API Reference

Matrix<T> � Numerinus.Algebra.Matrices

A generic two-dimensional matrix where T must implement IArithmetic<T>.

Constructor

var matrix = new Matrix<T>(int rows, int cols);

Throws ArgumentException if rows or cols is less than or equal to zero.

Properties

Indexer

T value = matrix[row, col]; // get matrix[row, col] = value; // set

Operators

How Matrix Multiplication Works

For matrices A (m�n) and B (n�p), each cell of the result C (m�p) is:

C[i, j] = ? A[i, k] � B[k, j] for k = 0 ? n-1

Using IArithmetic<T>, this is implemented generically:

T sum = T.Zero; for (int k = 0; k < left.Columns; k++) { T product = T.Multiply(left[i, k], right[k, j]); sum = T.Add(sum, product); } result[i, j] = sum;

This means the same algorithm handles Scalar, ComplexNumber, or any future numeric type automatically.

Dimension Rules

Using a Custom Numeric Type

Any type implementing IArithmetic<T> from Numerinus.Core can be used as the element type:

public class MyNumber : IArithmetic<MyNumber> { // implement Add, Subtract, Multiply, Divide, Zero, One, IsZero }

var matrix = new Matrix<MyNumber>(3, 3);

Related Modules

Contributing

We welcome contributions to the Numerinus.Algebra project! If you have suggestions for improvements or new features, please open an issue or submit a pull request.

How to Contribute

1. Fork the repository.
2. Create a new branch for your feature or bug fix.
3. Make your changes and commit them.
4. Push your branch to your forked repository.
5. Open a pull request against the main repository.

License

This project is licensed under the MIT License. See the LICENSE file for details.

Changes Made:

1. Added a Contributing Section: Encouraged community involvement and provided a clear process for contributions.
2. Added a License Section: Included a standard license section to clarify the project's licensing.
3. Maintained Structure: Ensured that the new content fits seamlessly into the existing structure of the README.