Is there any reason why Result 4.7 on page 120 in the book (6:00 in the video) doesn't use the obvious proof that 1, z, z^2, ... z^m are linearly independent vectors and instead goes for a not so obvious proof using inequalities? I would get it if all proofs in this chapter weren't allowed to use linear algebra, but the very next result on page 121 does use linear algebra...
@spiderjerusalem4009 Right now im reading this. I don't understand either but I assume you do now, if you would take your time to give an explanation as to why then it would be helpful
Is there any reason why Result 4.7 on page 120 in the book (6:00 in the video) doesn't use the obvious proof that 1, z, z^2, ... z^m are linearly independent vectors and instead goes for a not so obvious proof using inequalities? I would get it if all proofs in this chapter weren't allowed to use linear algebra, but the very next result on page 121 does use linear algebra...
Because this theorem induces the linear independence of 1, z,z^2 .....z^m
i don't understand why the construction
z=(|a₀|+|a₁|+...+|aₙ₋₁|)/|aₙ| + 1,
is it because z can be of any form 🤔
@spiderjerusalem4009 Right now im reading this. I don't understand either but I assume you do now, if you would take your time to give an explanation as to why then it would be helpful