Linked from

The 30 pages that link to Gaussian elimination, each with the reason it gives.

• DeterminantRelated: Tracking row-operation effects gives an efficient way to compute determinants.

• Linear algebraRelated: It reduces a system to a form where its solutions can be read or classified.

• Linear independenceRelated: Row reduction reveals whether each vector contributes a pivot or depends on earlier columns.

• Numerical stabilityRelated: Pivoting variants illustrate how algorithm design can control rounding-error growth.

• Identity matrixRelated: Row operations can transform a coefficient matrix toward the identity to expose its inverse or solve a system.

• System of linear equationsRelated: It systematically reduces the equations to expose their solutions or inconsistencies.

• Invertible matrixRelated: Row reduction can find an inverse by reducing the matrix to the identity.

• LU decompositionRelated: Its elimination steps produce the entries of the lower-triangular factor.

• Chinese mathematicsRelated: Classical rod arithmetic used elimination procedures closely resembling this algorithm.

• Rank (linear algebra)Related: Its pivots identify the independent rows that determine a matrix’s rank.

• Matrix inverseRelated: Row reduction can compute an inverse by transforming the matrix into the identity.

• Permutation matrixRelated: Row swaps can be represented and accumulated as multiplication by permutation matrices.

• The Nine Chapters on the Mathematical ArtRelated: The fangcheng procedure transforms arrays of coefficients to determine several unknowns.

• Column spaceRelated: Pivot columns identify a basis for the original matrix’s column space.

• Matrix theoryRelated: It solves systems and determines rank using elementary matrix operations.

• Atanasoff–Berry computerRelated: The computer was designed to solve systems of linear equations using this method.

• Sylvester's criterionRelated: Its pivots are ratios of successive leading principal minors.

• Triangular matrixRelated: Elimination transforms many systems into triangular form, enabling efficient back-substitution.

• John Vincent AtanasoffRelated: The ABC was designed to automate arithmetic for this method.

• Equation solvingRelated: Row operations systematically simplify linear systems without changing their solutions.

• Dimension theorem for vector spacesRelated: Its pivot and free-variable counts reveal rank and nullity.

• Rouché–Capelli theoremRelated: Row reduction makes both relevant ranks and any inconsistent row visible.

• Steinitz exchange lemmaRelated: Its pivot steps provide a computational counterpart to selecting independent vectors from a spanning list.