Transformation Meaning

Drag the column vectors a₁ and a₂. Notice how matrix A transforms the unit vectors into its columns, morphing the unit square into a parallelogram.

A =
1.00 0.50
0.20 1.00

Transforming Unit Vectors

A
1 0
=
1.00   0.50 0.20   1.00
1 0
=
1.00 0.20
A
0 1
=
1.00   0.50 0.20   1.00
0 1
=
0.50 1.00

Determinant & Area

| I | = 1 ↦ | A | = ad − bc
Det = +0.90
Area = 0.90

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Linear Algebra for Computer Science
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