Understand the subject
What are basis and dimension?
A basis is a smallest independent set that can build every vector in a span. Dimension is the number of basis directions.
Use it to remove redundant vectors without changing the span.
See the structure
What the calculation is doing
v₁v₂independent directions span a plane
Worked interpretation
Read the result in context
dimension(span)=rank
Interpret with care
Important boundary
A long input list can still span a low-dimensional space.
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
dimension(span{v₁,…,vₖ}) = rank([v₁ … vₖ])
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Dependent input vectors are omitted from the returned basis.
dimension(span{v₁,…,vₖ}) = rank([v₁ … vₖ])
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.
