Is the Intersection of Subspaces a Subspace?

Thread starter jeffreylze
Start date Jan 26, 2009
Tags

Subspaces

Click For Summary

To prove that the intersection of two subspaces K and H of a vector space V, denoted K∩H, is also a subspace of V, one must demonstrate that it satisfies the subspace criteria: it contains the zero vector, is closed under vector addition, and is closed under scalar multiplication. The discussion highlights confusion about the axioms relevant to subspaces and the definition of a subspace itself. Clarification on these points is essential for constructing a valid proof. Understanding these foundational concepts is crucial for successfully addressing the homework problem. The intersection of subspaces indeed forms a subspace of the original vector space.

Jan 26, 2009

jeffreylze

Homework Statement

Let H and K be subspaces of a vector space V. Prove that the intersection K\cap H is a subspace of V.

Homework Equations

The Attempt at a Solution

This, I have absolutely NO idea how and where to start. Are there any axioms which can be used to prove this?

Physics news on Phys.org

Jan 26, 2009

NoMoreExams

What does it mean to be a subspace of a vector space?

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

View full post »