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Transforming the unit square

The matrix sends the unit square OABC to the parallelogram OA′B′C′. The columns of the matrix are where i and j land.

Scroll over the plane to zoom. Drag the arrow tips to set the columns of the matrix directly; hold Shift for free placement.

Transformation matrix

T =

Entries accept things like 1/2, √3/2, -sqrt(2)/2 or cos(pi/6).

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What the matrix does

Type
The identity transformation

Images of the vertices