Determinant measures "scaling factor" of linear transformation. Zero determinant means transformation collapses dimensions.
Linear equations — det(A) ≠ 0 means unique solution exists.
Computer graphics — Area scaling in 2D transformations.
Physics — Cross product magnitude: |a × b| = |det([a; b])|.
Engineering — Stability analysis of systems.
Economics — Leontief model solvability.
Robotics — Manipulator singularity detection.
Machine learning — Covariance matrix invertibility.
Cryptography — Matrix cipher decryption.
Control theory — Controllability and observability.
Geometry — Triangle area from vertex coordinates.
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