Understand the subject
What is change of basis?
A change-of-basis matrix rewrites coordinates of the same geometric vector in another ordered basis.
Use it when a vector’s coordinate description changes but the underlying vector does not.
See the structure
What the calculation is doing
input vector× Aoutput vectorC[to←from]=Bto⁻¹Bfrom
Worked interpretation
Read the result in context
C[to←from]=Bto⁻¹Bfrom
Interpret with care
Important boundary
Basis order matters; swapping basis vectors changes coordinates.
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
C[to←from] = B_to⁻¹B_from
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Multiplying by this matrix converts from-basis coordinates into to-basis coordinates.
C[to←from] = B_to⁻¹B_from
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.
