Understand the subject
What is an orthogonal complement?
The orthogonal complement contains all vectors perpendicular to every vector in a given span.
Use it to find directions that have zero dot product with a whole subspace.
See the structure
What the calculation is doing
v₁v₂independent directions span a plane
Worked interpretation
Read the result in context
Col(A)⊥=Null(Aᵀ)
Interpret with care
Important boundary
Perpendicularity depends on the Euclidean dot product used by this calculator.
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
Col(A)⊥ = Null(Aᵀ)
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Every returned vector has zero dot product with every column of A.
Col(A)⊥ = Null(Aᵀ)
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.
