Linear maps (aka linear transforms – scales, rotations, and shears) are a type of homomorphism probably familiar to many. Linear maps are quite intuitively "str

Linear maps (aka linear transforms – scales, rotations, and shears) are a type of homomorphism probably familiar to many. Linear maps are quite intuitively "structure-preserving" – particularly, by definition they preserve vector-vector addition and scalar-vector multiplication: f(v + u) = f(v) + f(u) f(k * v) = k * f(v) Homomorphisms that are also invertible (ie. bijective) are called isomorphisms, a term which is perhaps slightly more often encountered.