query: When is the exponential map between matrices injective?
positive_passages.docid: 155266
positive_passages.text: Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
negative_passages.docid: 89553
negative_passages.text: proof that every finite matrix has an annihilating polynomial
negative_passages.docid: 138342
negative_passages.text: Proof of a matrix exponential identity
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
negative_passages.docid: 83970
negative_passages.text: Proof of an elementary property of Projection Operators
negative_passages.docid: 42941
negative_passages.text: Pair of adjoint functors and showing that two certain maps are inverses
negative_passages.docid: 127000
negative_passages.text: When does $V = \ker(f) \oplus \operatorname{im}(f)$?
negative_passages.docid: 71037
negative_passages.text: Is exponential map locally a diffeomorphism w.r.t. base point?
negative_passages.docid: 93776
negative_passages.text: Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?
negative_passages.docid: 83279
negative_passages.text: How can I find such a $z$? (Injectivity of $T(z) = \lambda z + \mu\bar{z}$)
negative_passages.docid: 62219
negative_passages.text: Under what conditions is the exponential map on a Lie algebra injective?
negative_passages.docid: 70606
negative_passages.text: Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique
negative_passages.docid: 61993
negative_passages.text: Why is $V^{\vee}\otimes W^{\vee}\longrightarrow (V\otimes W)^{\vee}$ always injective?
negative_passages.docid: 49977
negative_passages.text: Show that the collection of matrices which commute with every idempotent matrix are the scalar matrices
negative_passages.docid: 99685
negative_passages.text: Matrix exponential for Jordan canonical form
negative_passages.docid: 158349
negative_passages.text: Prove the map sending a matrix to it's inverse is continuous.
negative_passages.docid: 88153
negative_passages.text: Finding all inner products on $\mathbb{R}^2$ for which a given linear map is orthogonal