query: If $T\colon \mathbb R^n \to \mathbb R^n $ linear and $T^2 = kT$
positive_passages.docid: 18379
positive_passages.text: Linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T.$
negative_passages.docid: 152451
negative_passages.text: REVISITED $^2$: Does a solution in $\mathbb{R}^n$ imply a solution in $\mathbb{Q}^n$?
negative_passages.docid: 138653
negative_passages.text: Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
negative_passages.docid: 101467
negative_passages.text: Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.
negative_passages.docid: 24561
negative_passages.text: $\mathbb S_n$ as semidirect product
negative_passages.docid: 22149
negative_passages.text: How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
negative_passages.docid: 20467
negative_passages.text: Show that $(y_n)\in l^q$
negative_passages.docid: 39057
negative_passages.text: Check the differentiablity of $\theta :\mathbb R^2 \setminus\{(0,0)\}\to \mathbb R$
negative_passages.docid: 83713
negative_passages.text: If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
negative_passages.docid: 152379
negative_passages.text: If $V_1, V_2$ are $\mathbb{Q}$-vector spaces and $f \colon V_1 \to V_2$ is additive, then $f$ is $\mathbb{Q}$-linear
negative_passages.docid: 34670
negative_passages.text: What exactly is the fixed field of the map $t\mapsto t+1$ in $k(t)$?
negative_passages.docid: 64140
negative_passages.text: Find a bijection from $\mathbb R$ to $\mathbb R-\mathbb N$
negative_passages.docid: 38584
negative_passages.text: $T\colon L^2[0,1] \to L^2[0,1]$ be a bounded linear map of Hilbert spaces such that if $f\in L^2[0,1]$ is continuous then so is $Tf$.
negative_passages.docid: 145104
negative_passages.text: $T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$
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: 96363
negative_passages.text: How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?
negative_passages.docid: 94378
negative_passages.text: Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?