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The determinant of a matrix measures the area/volume of the parallelogram/parallelipiped determined by its columns.

Created over 8 years ago, updated 10 days ago

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.