Understand the subject
What does a determinant mean?
A determinant is the signed area or volume scale of a square linear transformation. Zero means some direction has collapsed.
Use it to test invertibility and measure signed scaling.
See the structure
What the calculation is doing
input vector× Aoutput vectordet([[a,b],[c,d]])=ad−bc
Worked interpretation
Read the result in context
det([[a,b],[c,d]])=ad−bc
Interpret with care
Important boundary
Determinants belong to square matrices; a zero determinant means no inverse.
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
det(A) is the signed volume scale of the linear transformation A.
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
det([[1,2],[3,4]]) = 1·4 − 2·3 = −2.
det(A) is the signed volume scale of the linear transformation 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.
