The determinant of a matrix representing a linear transformation indicates the factor by which volumes are scaled
Image: Pablo Picasso, PD-US, via Wikimedia Commons
the determinant tells you about volume scaling under a linear transformation
The determinant of a matrix representing a linear transformation indicates the factor by which volumes are scaled
Related concepts
List of unsolved problems in mathematics
Random points in high dimensions are nearly equidistant due to the uniform distribution of volume in high-dimensional space
Eigenvalues and eigenvectors
Eigenvectors are unchanged in direction by a linear transformation
Rotation matrix
Determinant of a 2x2 matrix: ad - bc
Principal component analysis
Eigenvectors point along maximum variance
Neural scaling law
Chinchilla scaling law: optimal model size scales linearly with compute budget
Cholesky decomposition
Cholesky decomposition factors A = LL^T for symmetric positive definite matrices
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