query: every real symmetric matrix has at least one real eigenvalue.
positive_passages.docid: 19649
positive_passages.text: A question about the proof of "a symmetric matrix has real eigenvalues".
negative_passages.docid: 12213
negative_passages.text: Similarity of real matrices over $\mathbb{C}$
negative_passages.docid: 35013
negative_passages.text: Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
negative_passages.docid: 7457
negative_passages.text: Prove that $J^+AJ$ has positive eigenvalues
negative_passages.docid: 30665
negative_passages.text: Elegant proofs that similar matrices have the same characteristic polynomial?
negative_passages.docid: 41932
negative_passages.text: Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
negative_passages.docid: 12955
negative_passages.text: Classification of $n\times n$ real matrices up to congruence
negative_passages.docid: 73952
negative_passages.text: Upper bound for the sum of absolute values of the eigenvalues
negative_passages.docid: 119999
negative_passages.text: A property of every real polynomial.
negative_passages.docid: 49158
negative_passages.text: Multiplicity of eigenvalues
negative_passages.docid: 33448
negative_passages.text: Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
negative_passages.docid: 75536
negative_passages.text: every eigenvalue of $T$ has only one corresponding eigenvector up to a scalar multiplication
negative_passages.docid: 37162
negative_passages.text: Prove that matrices have equal rank.
negative_passages.docid: 144082
negative_passages.text: Every $n\times n$ matrix is the sum of a diagonalizable matrix and a nilpotent matrix.
negative_passages.docid: 65432
negative_passages.text: Prove that every elementary matrix is invertible, and the inverse is again an elementary matrix.
negative_passages.docid: 128990
negative_passages.text: Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
negative_passages.docid: 149923
negative_passages.text: eigenvalues of A - aI in terms of eigenvalues of A