determinants #

Shows det(A) as the signed area scaling of the unit square under a 2×2 linear map. The animation cycles through elementary row operations (swap, scale, row-add) by left-multiplying with an operation matrix E, while a side panel numerically confirms multiplicativity det(EA)=det(E)·det(A). When the area collapses toward 0, it highlights singularity (non-invertibility).

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Detecting invertibility/singularity of linear systems (det=0 means no unique solution)
02.Computing area/volume scaling and orientation change under linear transformations (graphics/physics)
03.Change of variables in integrals and probability (Jacobian determinant)

technical notes #

Pure Canvas2D; uses a 2×2 matrix map of the unit square to a parallelogram (area equals det). Scene-based easing (3×1.2s) interpolates row-operation matrices E, computes A=E·A0, and displays det values to illustrate sign flip, scaling, invariance under row-add, and multiplicativity.

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