Understand the subject
What is a column space?
The column space is every output reachable by combining a matrix’s original columns.
Use it to test which target vectors a linear transformation can produce.
See the structure
What the calculation is doing
v₁v₂independent directions span a plane
Worked interpretation
Read the result in context
Col(A)=span of A’s columns
Interpret with care
Important boundary
Use pivot columns from the original matrix—not reduced columns—as a basis.
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
Pivot columns of RREF identify the corresponding basis columns of A.
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Use original columns, not the columns of the reduced matrix.
Pivot columns of RREF identify the corresponding basis columns of 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.
