Find a subspace W of F4 such that F4=U⊕W

Asked Dec 25 '18 at 06:10

Active Dec 25 '18 at 06:26

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The solution has been given here

Suppose $U = \{(x,x,y,y) \in \mathbb{F}^4 : x, y \in \mathbb{F}\}$

I understand that we first need to construct a $W$ that the sum is $F^4$ and show that $U\cap W=0$.

My question is it seems that after I constructed the $W$, $U\cap W=0$ should be true. Am I correct? Or there are some cases where it won't be true?

edited Dec 25 '18 at 06:26

asked Dec 25 '18 at 06:10

JOHN

1

Are you asking if $F^{4}=U+W$ automatically implies $U\cap W={0}$? That is not true since $W$ can be $F^{4}$. – Kavi Rama Murthy Dec 25 '18 at 06:14
I should be more specific. How about suppose: Suppose U={(x,x,y,y)∈F4:x,y∈F} – JOHN Dec 25 '18 at 06:25

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