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Linear Algebra Calculators
LU Decomposition Calculator

LU Decomposition Calculator

Free online LU Decomposition Calculator. Part of our comprehensive Math Calculators suite.

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About LU Decomposition Calculator

Our free online LU Decomposition Calculator is an essential tool for anyone working with linear algebra. This calculator efficiently computes the LU decomposition (Lower-Upper decomposition) of any square matrix, breaking it down into a lower triangular matrix (L) and an upper triangular matrix (U) such that A = LU. This powerful factorization method is fundamental in solving systems of linear equations, calculating determinants, and inverting matrices, especially in numerical analysis, engineering, and data science. Designed for students, educators, and professionals, our calculator simplifies complex computations, saving valuable time and ensuring accuracy in your mathematical endeavors. It provides a straightforward solution for tackling challenging matrix problems with ease.

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Space between columns, newline between rows

Determinant |A|

-2.00

Matrix Rank

2

LU Decomposition (L)

[ 1.00 0.00 ]
[ 3.00 1.00 ]

QR Decomposition (Q)

[ 0.32 0.95 ]
[ 0.95 -0.32 ]