query: Let $T : \mathbb R^n \rightarrow \mathbb R^m$ is a Linear Transformation. Prove that $\operatorname {im}(T)$ is a subspace of $\Bbb R^m$
positive_passages.docid: 145912
positive_passages.text: Whether the image is a subspace of a linear transformation
negative_passages.docid: 121047
negative_passages.text: Proof: Sum of dimension of orthogonal complement and vector subspace
negative_passages.docid: 102299
negative_passages.text: Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
negative_passages.docid: 78648
negative_passages.text: Find an orthonormal basis for the subspace of $\mathbb R^4$
negative_passages.docid: 55488
negative_passages.text: Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
negative_passages.docid: 79061
negative_passages.text: show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
negative_passages.docid: 59531
negative_passages.text: Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
negative_passages.docid: 141166
negative_passages.text: How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$ is injective, then $\phi$ is also injective?
negative_passages.docid: 44685
negative_passages.text: Inner product on $C(\mathbb R)$
negative_passages.docid: 131082
negative_passages.text: Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
negative_passages.docid: 103839
negative_passages.text: Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
negative_passages.docid: 100107
negative_passages.text: How can I prove that a linear map $T:V\to V$ such that $T^2 = I$ is equal to the Identity map?
negative_passages.docid: 62887
negative_passages.text: Proof that a linear transformation is continuous
negative_passages.docid: 50159
negative_passages.text: How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
negative_passages.docid: 81040
negative_passages.text: proof about commutative operators and T-cyclic vectors
negative_passages.docid: 65494
negative_passages.text: Proper subspaces of $ R^n $
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$