Recent content by calstudent

Inner Product Space Norm Thanks for the help so far. I'm trying to find the norm for the this inner product. So far I have: \Vert p\Vert=\sqrt{\left\langle p,p\right\rangle }=\sqrt{\intop_{0}^{1}p(z)\overline{p(z)}dz}=\sqrt{\intop_{0}^{1}|p(z)|^{2}dz} I also know that p(z) can be denoted...

p\in P_3(\mathbb{F}) What does \overline{p(z)} mean? I would guess that it's related to the complex conjugate, but I'm not sure. For context, I'm dealing with an inner product space defined by \langle p,q\rangle=\intop_{0}^{1}p(z)\overline{q(z)}dz Thanks!

But the fact that there exists a matrix P such that A'= P-1AP, is the direct definition of similarity and the proof would be trivial. Does it follow directly from the definition of JNF that such a matrix P always exists?

1. Show that two matrices A,B ∈ Mn(C) are similar if and only if they share a Jordan canonical form. 2. Prove or disprove: A square matrix A ∈ Mn (F) is similar to its transpose AT. If the statement is false, find a condition which makes it true. (I'm pretty sure that this is true and can be...