Gaussian Elimination
Gaussian elimination reduces a matrix to upper-triangular form via row operations to solve linear systems, with complexity O(n^3).
Purpose
To provide the fundamental algorithm for solving linear systems and inverting matrices.
Mechanism
Forward elimination: use row subtraction to zero out elements below each pivot, reaching upper-triangular form. Back substitution: solve from the last row upward. Partial pivoting (largest element) improves numerical stability.
Use cases
- Linear system solving
- Matrix inversion
- Linear algebra