Understand the subject
What is a matrix exponential?
The matrix exponential accumulates infinitely many repeated tiny linear transformations and is central to linear differential equations.
Use it for the bounded numerical operation e to the matrix A.
See the structure
What the calculation is doing
input matrix→bounded numerical method→labelled approximation
Worked interpretation
Read the result in context
eᴬ=I+A+A²/2!+A³/3!+…
Interpret with care
Important boundary
The result is an approximation with a stated numerical method and convergence boundary.
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
eᴬ = I + A + A²/2! + A³/3! + …
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
For a diagonal matrix, exponentiate each diagonal entry.
eᴬ = I + A + A²/2! + A³/3! + …
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.
