query: Let $T: \mathbb{R}^4 \to \mathbb{R}^4$ be any linear transformation. Then how can I show that $T$ has a proper non zero invariant subspace.
positive_passages.docid: 141794
positive_passages.text: Invariant subspaces of specific dimension
negative_passages.docid: 20879
negative_passages.text: Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
negative_passages.docid: 41013
negative_passages.text: Subspace of $C^3$ that spanned by a set over C and over R
negative_passages.docid: 150442
negative_passages.text: What does a linear transformation do to a vector in $\mathbb{R}^2$
negative_passages.docid: 149907
negative_passages.text: $T\circ T=0:V\rightarrow V \implies R(T) \subset N(T)$
negative_passages.docid: 74764
negative_passages.text: Dimension for a closed subspace of $C[0,1]$.
negative_passages.docid: 127488
negative_passages.text: If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
negative_passages.docid: 112024
negative_passages.text: Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
negative_passages.docid: 144097
negative_passages.text: eigenvalues and eigenvectors of $vv^T$
negative_passages.docid: 6202
negative_passages.text: $V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $?
negative_passages.docid: 24657
negative_passages.text: Let $T,S$ be linear transformations, $T:\mathbb R^4 \rightarrow \mathbb R^4$, such that $T^3+3T^2=4I, S=T^4+3T^3-4I$. Comment on S.
negative_passages.docid: 112939
negative_passages.text: Find a basis for the subspace of $\mathbb{R}^4$ spanned by the given vectors.
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 125785
negative_passages.text: Minimal polynomial of restriction to invariant subspace divides minimal polynomial
negative_passages.docid: 10042
negative_passages.text: How to Show that Linear transformation is invertible?
negative_passages.docid: 60684
negative_passages.text: Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
negative_passages.docid: 58595
negative_passages.text: Existence of a G-invariant matrix