query: $A v = \lambda v \implies A^* v = \bar{\lambda} v$ if $A$ is normal
positive_passages.docid: 157246
positive_passages.text: Adjoint matrix eigenvalues and eigenvectors
negative_passages.docid: 15300
negative_passages.text: How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
negative_passages.docid: 50130
negative_passages.text: $\operatorname{Aut}(V)$ is isomorphic to $S_3$
negative_passages.docid: 139096
negative_passages.text: $|AxA|$ is a constant implies normal subgroup
negative_passages.docid: 131998
negative_passages.text: let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
negative_passages.docid: 109682
negative_passages.text: Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
negative_passages.docid: 155579
negative_passages.text: Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
negative_passages.docid: 13899
negative_passages.text: Proof that $-v = (-1)*v$
negative_passages.docid: 80346
negative_passages.text: If every eigenvector of $T$ is also an eigenvector of $T^{*}$ then $T$ is a normal operator
negative_passages.docid: 18195
negative_passages.text: Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces
negative_passages.docid: 34702
negative_passages.text: Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
negative_passages.docid: 81176
negative_passages.text: A normal matrix with real eigenvalues is Hermitian
negative_passages.docid: 97158
negative_passages.text: Prove that the operator norm is a norm
negative_passages.docid: 58113
negative_passages.text: Av = Bv for all v implies A = B?
negative_passages.docid: 84535
negative_passages.text: The spectral radius of normal operator
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$