query: Is the operator invertible?
positive_passages.docid: 24657
positive_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: 6398
negative_passages.text: Can the product of an $4\times 3$ matrix and a $3\times 4$ matrix be invertible?
negative_passages.docid: 89057
negative_passages.text: How does one properly define the derivative of one operator-valued function?
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: 50664
negative_passages.text: Inverse function of $\operatorname{li}(x)$ over $x>\mu$?
negative_passages.docid: 108781
negative_passages.text: $A$ and $B$ are bounded linear operators from the normed linear space $X$ to itself. If $AB$ is invertible are $A$ and $B$ invertible?
negative_passages.docid: 36567
negative_passages.text: $A^{T}A$ positive definite then A is invertible?
negative_passages.docid: 5758
negative_passages.text: Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
negative_passages.docid: 118778
negative_passages.text: What's the inverse operation of exponents?
negative_passages.docid: 112900
negative_passages.text: Eigenvalue of a polynomial evaluated in a operator
negative_passages.docid: 3038
negative_passages.text: For positive invertible operators $C\leq T$ on a Hilbert space, does it follow that $T^{-1}\leq C^{-1}$?
negative_passages.docid: 151046
negative_passages.text: Closure of the invertible operators on a Banach space
negative_passages.docid: 45523
negative_passages.text: Can the product of two non invertible elements in a ring be invertible?
negative_passages.docid: 63475
negative_passages.text: Is there any connection between a matrix being invertible and being diagonalizable?
negative_passages.docid: 151752
negative_passages.text: Example of a linear operator on some vector space with more than one right inverse.
negative_passages.docid: 106540
negative_passages.text: Is this binary operation commutative?
negative_passages.docid: 69509
negative_passages.text: Showing a Linear Transformation is invertible