Understand the subject
What is Cholesky decomposition?
Cholesky factors a positive-definite symmetric matrix into a lower-triangular matrix times its transpose.
Use it only when the matrix is eligible and the symmetry/definiteness assumptions hold.
See the structure
What the calculation is doing
A=L×UA≈LLᵀ
Worked interpretation
Read the result in context
A≈LLᵀ
Interpret with care
Important boundary
A failure is not a generic error: it means the entered matrix does not meet this factorization’s conditions.
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
A ≈ LLᵀ
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
A non-positive pivot means the matrix is not positive definite.
A ≈ LLᵀ
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.
Numerical policy
Results use real double-precision arithmetic, a 1e-10 structural tolerance where stated, bounded iterations, and labelled approximations.
