Prove that if V = M (Direct sum) N, then

V/M (Isomorphisms.) N. Hint: Restrict the quotient mapping V /M to N and the kernel and image of the restricted mapping.

plx help(Crying)

Printable View

- Oct 28th 2010, 08:07 AMmathbeginnerDirect sum and Isomorphisms
Prove that if V = M (Direct sum) N, then

V/M (Isomorphisms.) N. Hint: Restrict the quotient mapping V /M to N and the kernel and image of the restricted mapping.

plx help(Crying) - Oct 28th 2010, 07:58 PMtonio

As any has a unique expression as , define by

Uniqueness of expression gives you that f is well defined, and now just prove that f is an isomorphism of vec. spaces.

Tonio

Pd. Of course, f is NOT an isomorphism! You need to find its kernel and use the fist isomorphism theorem - Oct 28th 2010, 08:22 PMDrexel28
- Oct 28th 2010, 09:50 PMmanygrams
Would you happen to be a uOttawa student? I have that same question on an assignment of mine