Understand the subject
What does rank count?
Rank counts independent directions carried by a matrix. It equals the number of pivots in RREF.
Use it to detect dependence and determine space dimensions.
See the structure
What the calculation is doing
v₁v₂independent directions span a plane
Worked interpretation
Read the result in context
rank(A)=number of pivots
Interpret with care
Important boundary
Numerical rank depends on a disclosed tolerance; exact rank does not.
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
rank(A) = number of pivots in RREF(A)
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Rank counts independent rows and also independent columns.
rank(A) = number of pivots in RREF(A)
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.
