can anyone help with these questions?! woudl really appreciate it , finding them impossible!

 

a linear transformation T: R^6 --> R^6 is known to have characteristic polynomial

 

x^2 (x + 1) (x+5)^3

 

determine all possibilities for the mimimum polynomial of T

 

Let V be and inner product space over C (complex) with inner product space <,> and let u,v, be vectors from V which are orthogonal to each other . prove that

||au+bV||^2 = |a|^2 ||u||^2 + |b|^2 ||v||^2

 

for any complex numbers a and b.

 

thank you!!!!

what is the definition of minimal polynomial? what can you say about it with respect to the characteristic poly? and if you know that an inner product is a (complex conjugate) bilinear form then what's the problem with the second part? I mean waht is ||x||^2 in terms of the inner product?