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The determinant scales the area of any measurable planar figure, not just squares. The absolute value of the determinant acts as a uniform area scaling factor for all regions under the linear transformation.
Conditions: The transformation is linear.; The figure is measurable and has finite area.; Use ordinary Euclidean area in standard orthonormal coordinates.
The determinant scales the area of any measurable planar figure, not just squares. The absolute value of the determinant acts as a uniform area scaling factor for all regions under the linear transformation.
Conditions: The transformation is linear.; The figure is measurable and has finite area.; Use ordinary Euclidean area in standard orthonormal coordinates.