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[jessica]

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!!!!

[matt grime]

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?