Understand the subject
What is LDL transpose decomposition?
LDL transpose separates a symmetric matrix into unit lower-triangular, diagonal, and transposed factors without square roots.
Use it for eligible symmetric matrices under this page’s exact no-pivoting contract.
See the structure
What the calculation is doing
A=L×UA=LDLᵀ
Worked interpretation
Read the result in context
A=LDLᵀ
Interpret with care
Important boundary
A zero computed diagonal pivot is unsupported here because pivoting is deliberately excluded.
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 = LDLᵀ
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
L is unit lower triangular and D is diagonal.
A = LDLᵀ
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.
Supported scope
This exact educational contract uses no pivoting and rejects a zero computed diagonal pivot.
