Week4Lecture3: Möbius transformatios, part I

[shacharh]

Another way to show it's a bijcetion: You can define a mobius tra. using an invertible 2x2 matrix (a b c d), then show that composition of Mobious trs respects multiplication of matrices - if T is the transformation using matrix A and S using B then T after S is the transformation defined by (AB).
As a corrolary, a Mobius transformation is invertible - its inverse is the trans. defined with the inverse matrix - so it's a bijection.

[personxy]

Teacher, why we called it linear?(A linear function is T(ax+b)=aT(x)+b, but it is not

[CornishMiner]

Right at the end, a division by zero of a non-zero number is defined as infinity. Not sure that it was made clear that in C ∪ {∞} z/0 = ∞ and z/∞ = 0, and that ∞/0 = ∞ and 0/∞ = 0, leaving 0/0 and ∞/∞ undefined.

[esmirhodzic]

thank yoou for so awesome videos :D really helpful