Understand the subject
What is a matrix power?
A positive matrix power applies the same square transformation repeatedly.
Use it for repeated linear steps and recurrence-style transformations.
See the structure
What the calculation is doing
1234
row 1 · column 12012
1×2 + 2×1 = 4Worked interpretation
Read the result in context
A⁰=I; Aⁿ=A×A×…×A
Interpret with care
Important boundary
Negative powers require an inverse, so singular matrices cannot support them.
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
A⁰ = I; A⁻ⁿ = (A⁻¹)ⁿ
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
For A = [[1,1],[0,1]], A³ = [[1,3],[0,1]].
A⁰ = I; A⁻ⁿ = (A⁻¹)ⁿ
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.
