Question

x, y,\(\in P_n\)
w(x,y) = x(1) y(1) is a bilinear form
How to check whether it is degenerate or non- degenerate?
Please, help

Answer 1

i need to check the text book :o

Answer 2

Please!!:)

Answer 3

brb :D
ill solve it for u and ill type it when i finish ok ?

Answer 4

to find if its non- degenerate
we check the isomorphism,
Dedinition of group isomorphism
An isomorphism\(\phi\) from a group G to a group G' is a one-to-one mapping (or function) from G onto G' that preserves the group operation that is,
\(\phi(ab)=\phi(a)\phi(b)\) for all a,b in G
......

Answer 5

so u have function
w(x,y)=x(1)y(1)
since x,y belong to P_n
p_n={all set of primes <n}
x(1)=0
y(1)=0
w(x,y)=0 _so its isomorphism
its non- degenerate

Answer 6

Thanks a lot

Answer 7

np :)