📐 Intersection of Subspaces
The intersection of any collection of subspaces of $V$ is a subspace of $V$.
Proof: Let $\\{W_i\\}_{i \\in I}$ be subspaces of $V$ and let $W = \\bigcap_{i \\in I} W_i$.
- **Non-empty:** Each $W_i$ contains $\\mathbf{0}$, so $\\mathbf{0} \\in W$.
- **Closure under addition:** If $u, v \\in W$, then $u, v \\in W_i$ for all $i$. Since each $W_i$ is a subspace, $u + v \\in W_i$ fo...
From: Advanced Linear Algebra
Learn more: https://advanced-linalg.vercel.app/#/section/3
Explore all courses: https://mathacademy-cyan.vercel.app