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Kapittel 2 · Lineærtransformasjonerlinear transformations

The Determinant as Area

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A 2×2 matrix maps the unit square to a parallelogram whose signed area is det A = ad − bc. A continuous morph from identity to A shows the deformation; scrubbing one entry through det = 0 collapses the parallelogram to a line, then flips orientation as det goes negative.

determinantsigned areaorientationlinear transformationunit squaresingular matrix
ForutsetterLinear Transformations: A Matrix Moves the GridA Matrix Is a Function: T(v) = Av