query: Characterizing spectral radius using invertible elements in unital $C^*$ algebra
positive_passages.docid: 150287
positive_passages.text: Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$
negative_passages.docid: 136909
negative_passages.text: Functional Analysis: The rank of an operator detemines if it's a compact operator.
negative_passages.docid: 154837
negative_passages.text: mapping properties of $(1−z)^i$
negative_passages.docid: 18585
negative_passages.text: Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
negative_passages.docid: 136643
negative_passages.text: Continuity of eigenvalues and spectral radius for a general matrix
negative_passages.docid: 150714
negative_passages.text: Quick question: matrix with norm equal to spectral radius
negative_passages.docid: 55018
negative_passages.text: Prove that $A^*A + I$ is invertible
negative_passages.docid: 141286
negative_passages.text: When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
negative_passages.docid: 39334
negative_passages.text: Non-degenerate bilinear forms and invertible matrices
negative_passages.docid: 22297
negative_passages.text: Normal operator $\Rightarrow$ S invariant implies $S^\perp$ invariant
negative_passages.docid: 74128
negative_passages.text: Second exterior power of a complex vector space
negative_passages.docid: 48291
negative_passages.text: Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
negative_passages.docid: 75215
negative_passages.text: Properties of invertible matrices
negative_passages.docid: 29756
negative_passages.text: Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
negative_passages.docid: 59055
negative_passages.text: Diagonalizable transformation restricted to an invariant subspace is diagonalizable
negative_passages.docid: 66299
negative_passages.text: Operator whose spectrum is given compact set
negative_passages.docid: 127000
negative_passages.text: When does $V = \ker(f) \oplus \operatorname{im}(f)$?