the Nature of Linear Transformation
what's a linear function? (aka linear map, linear transformation.)
by definition, it's a function f on vector space such that:
f[x + y] == f[x] + f[y] f[α x] == α f[x]
where α is a scalar.
but what does it mean intuitively?
- The zero vector is never moved.
- The transform is linear in nature. Meaning, kinda uniform thru-out, as in uniform scaling. It includes isometries of {rotation, reflection, scaling} but does not include translation (because that moves the zero vector)