query: Why are the eigenvalues of symmetric real matrices real?
positive_passages.docid: 19649
positive_passages.text: A question about the proof of "a symmetric matrix has real eigenvalues".
negative_passages.docid: 135316
negative_passages.text: A basic question on diagonalizability of a matrix
negative_passages.docid: 49158
negative_passages.text: Multiplicity of eigenvalues
negative_passages.docid: 87318
negative_passages.text: Why are symmetric positive definite (SPD) matrices so important?
negative_passages.docid: 116539
negative_passages.text: Eigenvalues of matrix satisfying $A^2 = A$
negative_passages.docid: 108132
negative_passages.text: How Do I Compute the Eigenvalues of a Small Matrix?
negative_passages.docid: 54099
negative_passages.text: What are the eigenvalues of $\operatorname{ad}x$?
negative_passages.docid: 153127
negative_passages.text: Is $U=V$ in the SVD of a symmetric positive semidefinite matrix?
negative_passages.docid: 50948
negative_passages.text: When Eigenfunctions/Wavefunctions are real?
negative_passages.docid: 22222
negative_passages.text: Properties of zero-diagonal symmetric matrices
negative_passages.docid: 122951
negative_passages.text: If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?
negative_passages.docid: 18939
negative_passages.text: Eigenvalues of the transpose
negative_passages.docid: 102152
negative_passages.text: Eigensystem, Eigenvalue doesn't output nonreal eigenvalues
negative_passages.docid: 157246
negative_passages.text: Adjoint matrix eigenvalues and eigenvectors
negative_passages.docid: 156868
negative_passages.text: Why is finding $M$ eigenvectors on smaller matrix valid?
negative_passages.docid: 139557
negative_passages.text: Why are the eigenvectors of the Laplacian of a ring graph sinusoidal?
negative_passages.docid: 52260
negative_passages.text: Diagonalization and eigenvalues