The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.
Created almost 9 years ago, updated 5 months ago
ID23746
Theorem: The absolute value of the determinant of a matrix measures the area (2D), volume (3D), or hypervolume (nD) of the parallelogram/parallelepiped determined by its columns. If $A$ maps the unit cube, then $|\det(A)|$ is the volume of the image.
**Theorem:** The absolute value of the determinant of a matrix measures the area (2D), volume (3D), or hypervolume (nD) of the parallelogram/parallelepiped determined by its columns. If $A$ maps the unit cube, then $|\det(A)|$ is the volume of the image.