Daily assignment for April 7

• For a reference about today's lecture, see pp. 156–158 of Needham.
• Prove that if \( H \) is a 2×2 Hermitian matrix (meaning \( \bar H = H^T \) and \( M \) is any complex matrix then \( \bar M^T H M \) is a Hermitian matrix. Use this to prove that Möbius transformations send circles and lines to circles and lines. (Represent the circle or line as the set of \( Z \) such that \( \bar Z^T H Z = 0 \) and use the fact that applying a Möbius transformation to \( Z \) is the same as multiplying by an invertible 2×2 complex matrix \( M \).)
• Post your work on Canvas.