Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $R$, $S$, and $T$ be subspaces of a vector space.
I was able to show that $(R \cap T)+(S \cap T) \subseteq (R+S) \cap T$.

So my question now is: When will equality happen without using the other inclusion?

share|cite|improve this question
What does "without using the other inclusion" exactly mean? – Maikel Dec 11 '12 at 13:30
Since it was established that $(R \cap T)+(S \cap T) \subseteq (R+S) \cap T$. I mean not to use this inclusion $(R \cap T)+(S \cap T) \supseteq (R+S) \cap T$ to establish the equality. In other words, what should be the sufficient hypothesis for it to be equal. Thanks. – Philip Benj Marcoby Eragon Dec 11 '12 at 13:48
If your vector space is a finite dimensional vector space with an inner product, the two sides are the same. – user1551 Dec 12 '12 at 0:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.