query: Spectrum of a positive operator
positive_passages.docid: 100731
positive_passages.text: Positive operator has a positive spectrum?
negative_passages.docid: 73807
negative_passages.text: Prove positive definiteness
negative_passages.docid: 73406
negative_passages.text: Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
negative_passages.docid: 59402
negative_passages.text: Comparing Eigenvalues of Positive Semidefinite Matrices
negative_passages.docid: 136909
negative_passages.text: Functional Analysis: The rank of an operator detemines if it's a compact operator.
negative_passages.docid: 5058
negative_passages.text: Eigenvalues of the rank one matrix $uv^T$
negative_passages.docid: 110271
negative_passages.text: Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
negative_passages.docid: 7457
negative_passages.text: Prove that $J^+AJ$ has positive eigenvalues
negative_passages.docid: 119775
negative_passages.text: Density of finite rank operator in compact operators on Hilbert spaces
negative_passages.docid: 59632
negative_passages.text: Bessel's function in spectral geometry
negative_passages.docid: 20415
negative_passages.text: Show that the integral of a positive function is positive
negative_passages.docid: 67344
negative_passages.text: What is spectrum for Laplacian in $\mathbb{R}^n$?
negative_passages.docid: 11109
negative_passages.text: The ideal generated by a non-compact operator
negative_passages.docid: 153127
negative_passages.text: Is $U=V$ in the SVD of a symmetric positive semidefinite matrix?
negative_passages.docid: 119352
negative_passages.text: compact and self adjoint square root of an operator
negative_passages.docid: 106097
negative_passages.text: Spectrum of the sum of two commuting matrices
negative_passages.docid: 93062
negative_passages.text: Is Every Invariant Subspace the Kernel of an polynomial applied in the operator?