Determine intersection dimension of two 4D subspaces
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: Medium
Interview Round: Technical Screen
Let Y and M be 4-dimensional subspaces of a 7-dimensional vector space X over R. Using dim(Y) + dim(M) = dim(Y + M) + dim(Y ∩ M), determine all possible values of dim(Y ∩ M). Among {0, 1, 2, 3}, which value cannot occur for dim(Y ∩ M)? Prove your answer and give an explicit construction for one attainable case.
Quick Answer: This question evaluates linear algebra skills—specifically understanding of subspace dimensions, intersections and sums, and the dimension formula for subspace sums and intersections—within the Statistics & Math domain.
