What is Matrix Decompositions LU QR Calculator and Why it Matters?
LU and QR factorizations are core tools in numerical linear algebra for solving systems and least-squares problems.
Mathematical Formula and Theory
LU writes A = L U (with possible permutation). QR writes A = Q R with Q orthogonal and R upper-triangular.
How to Use This Calculator - Step by Step
- Select matrix size and enter entries.
- Choose LU or QR.
- Click Decompose.
Solved Example with Full Calculation
A = [[2,1],[4,3]]. LU: L = [[1,0],[2,1]], U = [[2,1],[0,1]]. Verification: L U = A.