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)

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- Oct 28th 2010, 09:07 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, 08:58 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, 09:22 PMDrexel28
- Oct 28th 2010, 10:50 PMmanygrams
Would you happen to be a uOttawa student? I have that same question on an assignment of mine