Determinant
The determinant of a square matrix is the signed volume scaling factor of its linear transformation. A zero determinant indicates singularity.
Definition
The determinant of a square matrix is the signed volume scaling factor of its linear transformation. A zero determinant indicates singularity.
Intuition
Its sign indicates orientation; its magnitude indicates volume change.
Worked example
For rows (2, 1) and (3, 4), det(A) = 2 × 4 − 1 × 3 = 5.
The math
For a 2 by 2 matrix, . Also .
In machine learning
Determinants help with geometry and symbolic analysis; a raw determinant is a poor numerical test of near-singularity.
Sources
More in Linear algebra
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