Linked from

The 14 pages that link to LU decomposition, each with the reason it gives.

• Gaussian eliminationCompared with: It packages elimination steps for solving multiple systems with the same coefficient matrix.

• Numerical stabilityRelated: Its computed factors can be judged by whether they represent a nearby matrix accurately.

• Singular value decompositionCompared with: LU supports efficient linear-system solving but does not provide orthogonal directions or optimal low-rank truncation.

• System of linear equationsRelated: It reuses a factorization to solve multiple systems with the same coefficients.

• Invertible matrixRelated: Solving against these factors computes inverse actions without forming the inverse explicitly.

• QR decompositionCompared with: LU uses triangular factors without requiring an orthogonal transformation.

• Direct methodRelated: It expresses elimination as reusable matrix factors, especially when solving systems with multiple right-hand sides.

• Matrix inverseCompared with: It computes solutions efficiently without explicitly constructing the inverse.

• Permutation matrixRelated: Pivoting is recorded by a permutation matrix in the factorization.

• Cramer's ruleCompared with: It reuses matrix factors across multiple right-hand sides, unlike repeated Cramer determinants.

• Matrix theoryBroader topic: It turns repeated linear-system solves into efficient triangular substitutions.

• Laplace expansionCompared with: The factorization yields determinants efficiently without recursively expanding minors.

• Fundamental theorem of linear algebraCompared with: It is a computational factorization, not a statement about subspace orthogonality.

• Triangular matrixBroader topic: It represents a matrix through two triangular factors and supports repeated linear solves.