query: Linear operator such that $N(T)=R(T)$
positive_passages.docid: 26665
positive_passages.text: When does the kernel of a function equal the image?
negative_passages.docid: 144048
negative_passages.text: Linear Operators satisfying $S^n=0$ but $S^{n-1}\neq 0$
negative_passages.docid: 51313
negative_passages.text: Extension of linearly independent set to a basis in an infinite dimensional vector space
negative_passages.docid: 14550
negative_passages.text: Every Hilbert space has an orthonomal basis - using Zorn's Lemma
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 105686
negative_passages.text: Time-ordered operator in Srednicki
negative_passages.docid: 65395
negative_passages.text: Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
negative_passages.docid: 151046
negative_passages.text: Closure of the invertible operators on a Banach space
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: 11159
negative_passages.text: Problem about a compact operator $T:l^p\rightarrow l^p$
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 17031
negative_passages.text: Idempotent linear operators are projections
negative_passages.docid: 56102
negative_passages.text: Prove that there is no non-zero linear operator on $\mathbb C^{2}$ such that $(\alpha | T\alpha) = 0$
negative_passages.docid: 108329
negative_passages.text: If $T\alpha=c\alpha$, then there is a non-zero linear functional $f$ on $V$ such that $T^{t}f=cf$
negative_passages.docid: 155509
negative_passages.text: Does a linear operator obeying Leibniz rule imply it is a differential operator?
negative_passages.docid: 93121
negative_passages.text: How to prove there exists a linear transformation?
negative_passages.docid: 75059
negative_passages.text: Let $T:\mathbb{R}^n\to \mathbb{R}^n$ be a linear transformation...