query: How to prove that the element-wise exponential of a symmetric matrix is not always positive-definite?
positive_passages.docid: 143793
positive_passages.text: If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite
negative_passages.docid: 48238
negative_passages.text: Prove the positive definiteness of Hilbert matrix
negative_passages.docid: 131596
negative_passages.text: Symmetric Inequality in $\mathbb{R}$
negative_passages.docid: 124001
negative_passages.text: Are the eigenvalues of the sum of two positive definite matrices increased?
negative_passages.docid: 91409
negative_passages.text: Semi positive definite matrix is always positive definite matrix
negative_passages.docid: 153372
negative_passages.text: Characterization of positive definite matrix with principal minors
negative_passages.docid: 99600
negative_passages.text: Show that a 2x2 matrix A is symmetric positive definite if and only if A is symmetric, trace(A) > 0 and det(A) > 0
negative_passages.docid: 114208
negative_passages.text: Does non-symmetric positive definite matrix have positive eigenvalues?
negative_passages.docid: 70606
negative_passages.text: Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique
negative_passages.docid: 85550
negative_passages.text: Positive definiteness of difference of inverse matrices
negative_passages.docid: 10478
negative_passages.text: Matrix reciprocal positive to prove $λ_{max⁡}=n$
negative_passages.docid: 145396
negative_passages.text: Symmetric Matrix , Eigenvectors are not orthogonal to the same eigenvalue.
negative_passages.docid: 13723
negative_passages.text: Doubly stochastic matrix proof
negative_passages.docid: 88386
negative_passages.text: Derivative of matrix exponential at $0$
negative_passages.docid: 104413
negative_passages.text: Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?
negative_passages.docid: 117175
negative_passages.text: Proof that the 2-norm of orthogonal transformation of a matrix is invariant
negative_passages.docid: 138342
negative_passages.text: Proof of a matrix exponential identity