query: If every vector is an eigenvector, the operator must be a scalar multiple of the identity operator?
positive_passages.docid: 35013
positive_passages.text: Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
negative_passages.docid: 21885
negative_passages.text: Why is the determinant useful when finding eigenvectors?
negative_passages.docid: 34539
negative_passages.text: How to intuitively understand eigenvalue and eigenvector?
negative_passages.docid: 10828
negative_passages.text: If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue
negative_passages.docid: 99942
negative_passages.text: A normal, idempotent linear operator must be self-adjoint
negative_passages.docid: 715
negative_passages.text: How do I prove that in every commuting family there is a common eigenvector?
negative_passages.docid: 98323
negative_passages.text: If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
negative_passages.docid: 80022
negative_passages.text: Eigenvector of A by $A^2$
negative_passages.docid: 14320
negative_passages.text: How to prove that eigenvectors from different eigenvalues are linearly independent
negative_passages.docid: 60990
negative_passages.text: Tricky operator identity: $[L^2,[L^2,\vec{r}]]=2 \hbar ^2 \{ L^2, \vec{r}\}$?
negative_passages.docid: 3544
negative_passages.text: Eigenvectors of a circulant matrix
negative_passages.docid: 56670
negative_passages.text: The intuition behind generalized eigenvectors
negative_passages.docid: 77388
negative_passages.text: Differentiation operator and eigenvalues
negative_passages.docid: 128453
negative_passages.text: If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
negative_passages.docid: 34820
negative_passages.text: Transpose Operator is diagonalizable?
negative_passages.docid: 13640
negative_passages.text: What is the importance of eigenvalues/eigenvectors?
negative_passages.docid: 37867
negative_passages.text: If $0$ is the only eigenvalue of a linear operator, is the operator nilpotent