Matrices as transformations
2×2 matrices represent linear maps: rotation, reflection, enlargement, shear.
Multiplying a column vector by a 2×2 matrix transforms it. Standard transformations have known matrix forms.
Worked examples
Rotation by θ: (cosθ −sinθ; sinθ cosθ).
Reflection in y = x: (0 1; 1 0).
Enlargement scale k: (k 0; 0 k) = kI.
Frequently asked questions
Composition of transformations?
Matrix product. Order: A·B applies B first, then A.
Determinant interpretation?
Area scale factor (signed). Negative det = orientation flips.