Understand the subject
What is a pseudoinverse?
The Moore–Penrose pseudoinverse extends inverse-like solving to rectangular or rank-deficient matrices through SVD.
Use it for the supported minimum-norm or least-squares relationship when an ordinary inverse does not exist.
See the structure
What the calculation is doing
A=L×UA⁺=VΣ⁺Uᵀ
Worked interpretation
Read the result in context
A⁺=VΣ⁺Uᵀ
Interpret with care
Important boundary
It is not an ordinary inverse, and tolerance controls which singular values are treated as usable.
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⁺ = VΣ⁺Uᵀ
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
The pseudoinverse supports rectangular and rank-deficient matrices.
A⁺ = VΣ⁺Uᵀ
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.
