Linear Algebra
Solve linear systems and compute determinants and ranks with Gaussian elimination.
4 articles~31 min total
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Matrices
- Gaussian Elimination: Solving Linear SystemsSolve a system of linear equations in O(n³): pivoting, the degenerate cases (no solution, infinitely many), exact arithmetic with fractions, modular systems and GF(2) systems with bitmasks.11 minIntermediate
- Determinant by Gaussian EliminationCompute the determinant in O(n³) by triangularizing the matrix, exactly with fractions, modulo a prime, and with integers only using the Bareiss algorithm.7 minIntermediate
- LU Decomposition and the Kraut MethodFactor a matrix as A = L·U, read the determinant off the diagonal of U, and reuse the factors to solve many right-hand sides.6 minIntermediate
- Rank of a MatrixFind the rank of a matrix by elimination, exactly, modulo a prime and over GF(2) with an XOR basis.7 minIntermediate