Let \(V_1,V_2,\ldots\) be countably many \(k\)-dimensional subspaces of \(\mathbb{R}^n\). Prove that there exists an \((n-k)\)-dimensional subspace \(W\) of \(\mathbb{R}^n\) such that \(\dim V_i\cap W=0\) for all \(i\).
GD Star Rating
loading...
2016-20 Finding a subspace,
loading...