Understand the subject
What are coordinates in a basis?
Coordinates tell how much of each ordered basis vector is needed to build a vector.
Use it to express one vector relative to a nonstandard independent basis.
See the structure
What the calculation is doing
input vector× Aoutput vector[v]ᴮ=B⁻¹v
Worked interpretation
Read the result in context
[v]ᴮ=B⁻¹v
Interpret with care
Important boundary
The basis must be square and independent for a unique coordinate vector.
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
[v]ᴮ = B⁻¹v
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Place the basis vectors in B’s columns and v in one column.
[v]ᴮ = B⁻¹v
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.
