query: $\Bbb{R}^3$ and a three dimensional subspace of $\Bbb{R^4}$
positive_passages.docid: 84148
positive_passages.text: Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$?
negative_passages.docid: 84871
negative_passages.text: Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 86309
negative_passages.text: Whether the set $A$ is a compact subset of $M_3(\Bbb R)$.
negative_passages.docid: 89517
negative_passages.text: Do four dimensional vectors have a cross product property?
negative_passages.docid: 78648
negative_passages.text: Find an orthonormal basis for the subspace of $\mathbb R^4$
negative_passages.docid: 86224
negative_passages.text: The root system of $sl(3,\mathbb C)$
negative_passages.docid: 123665
negative_passages.text: A question in Subspaces in linear algebra
negative_passages.docid: 125212
negative_passages.text: How to Show that the Only Subspaces of $R^2$ are the zero subspace, $R^2$ itself, and the lines through the origin
negative_passages.docid: 79285
negative_passages.text: Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 73773
negative_passages.text: $C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
negative_passages.docid: 73690
negative_passages.text: If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
negative_passages.docid: 723
negative_passages.text: Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
negative_passages.docid: 26764
negative_passages.text: Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
negative_passages.docid: 107520
negative_passages.text: Krull dimension of $\mathbb{C}[x_1, x_2, x_3, x_4]/\left$
negative_passages.docid: 135814
negative_passages.text: Prove certain subsets of $\mathbb R^n$ are subspaces