Understand the subject
What is LU decomposition?
LU decomposition records elimination as a lower-triangular multiplier matrix and an upper-triangular result, with pivoting tracked separately.
Use it to solve repeated systems with the same square coefficient matrix.
See the structure
What the calculation is doing
A=L×UPA=LU
Worked interpretation
Read the result in context
PA=LU
Interpret with care
Important boundary
The permutation matrix matters: omitting it can describe the wrong factorization.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Set the matrix dimensions required by the task.
- Fill every visible entry and any operation-specific control.
- Read the result type, factors, classification, and disclosed limitations.
Calculation method
Apply the stated linear-algebra contract
PA = LU
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
P records row swaps, L stores multipliers, and U is upper triangular.
PA = LU
Supported inputs
Precision and limits
Matrix size
Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.
Entry precision
Enter signed finite decimals with at most 30 digits and 15 decimal places.
Exactness
Finite decimals become reduced rational numbers and intermediate structural calculations are not rounded.
