Matrix Determinant Calculator
Calculate the determinant of a square matrix used in linear algebra operations.
About Matrix Determinant Calculator
The determinant of a square matrix is a scalar value that indicates whether the matrix is invertible (non-zero determinant) and represents the signed volume scaling factor of the linear transformation. For a 2×2 matrix [[a,b],[c,d]], det = ad − bc.
Formula
2×2 Determinant
det([[a,b],[c,d]]) = a*d - b*c
- a,b,c,d
- Elements of the 2×2 matrix
Worked example
With the default values below, Matrix Determinant Calculator returns Determinant of -14.000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- a (row1,col1)
- 3
- b (row1,col2)
- 8
- c (row2,col1)
- 4
- d (row2,col2)
- 6
Results
- Determinant
- -14.000000
Step by step
- 1det = a×d − b×c= -14.000000
- 2Singular?= No
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What does a zero determinant mean?
A zero determinant means the matrix is singular (non-invertible) and the transformation it represents collapses at least one dimension — the rows or columns are linearly dependent.
How is the determinant used in ML?
Determinants appear in Gaussian distributions (normalization constant involves det of covariance matrix), in checking rank of feature matrices, and in volume-preserving normalizing flows.