Gauss-Jordan Elimination - #12876
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cclauss merged 4 commits intoSep 13, 2026
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to solve a system of linear equations represented by Ax = b. The function reduces the coefficient matrix A to its reduced row echelon form (RREF) and transforms the RHS vector b accordingly. It includes: - Input validation for dimension compatibility - Full support for floating-point matrices - Doctests demonstrating example use cases and expected output
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Added a reference link to the Gaussian elimination Wikipedia page.
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Describe your change:
This pull request adds a complete implementation of the Gauss–Jordan elimination algorithm for solving systems of linear equations of the form Ax= b . The function reduces the coefficient matrix to Reduced Row Echelon Form (RREF) while applying the same transformations to the right-hand-side vector.
Key highlights of the change:
Implements a robust algorithm with pivot detection, row swaps, normalization, and elimination
Handles both consistent and singular systems gracefully
Performs validation to ensure input shape compatibility
Includes doctests that verify correctness.
Written to be readable and educational, aligning with the goals of TheAlgorithms/Python repository.
This function is a core algorithm in linear algebra and complements existing matrix utilities in the repository.
Checklist: