query: Translation of travelling wave is again a travelling wave, thus $0$ is an eigenvalue: Why?
positive_passages.docid: 29022
positive_passages.text: Linearization of PDE: $0$ is an eigenvalue since all translates of travelling waves are also travelling waves
negative_passages.docid: 70455
negative_passages.text: Why are all nonzero eigenvalues of the skew-symmetric real matrices pure imaginary?
negative_passages.docid: 45527
negative_passages.text: Do real matrices always have real eigenvalues?
negative_passages.docid: 13727
negative_passages.text: Wave equation: $y=A \sin(\omega t-kx)$ or $y=A\sin(kx-\omega t)$?
negative_passages.docid: 62845
negative_passages.text: If two operators commute, does it mean that every eigenfuction of one is also an eigenfunction of the other?
negative_passages.docid: 50948
negative_passages.text: When Eigenfunctions/Wavefunctions are real?
negative_passages.docid: 88349
negative_passages.text: Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
negative_passages.docid: 136643
negative_passages.text: Continuity of eigenvalues and spectral radius for a general matrix
negative_passages.docid: 128875
negative_passages.text: Expectation values of the position operator is equal to zero in case of even potentials?
negative_passages.docid: 117791
negative_passages.text: Why does the frequency of a wave remain constant?
negative_passages.docid: 42334
negative_passages.text: Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
negative_passages.docid: 98323
negative_passages.text: If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
negative_passages.docid: 9250
negative_passages.text: Can the zero vector be an eigenvector for a matrix?
negative_passages.docid: 11715
negative_passages.text: Prove that if $\langle Tx,x\rangle =0$ for all $x \in X$, then $T = 0$
negative_passages.docid: 90064
negative_passages.text: What does it mean when Mathematica returns a zero "eigenvector"?
negative_passages.docid: 88813
negative_passages.text: SphericalHarmonicY does not seem to be an eigenfunction of the spherical harmonic equation
negative_passages.docid: 127329
negative_passages.text: A problem about wave equation