query: Proving a nilpotent matrix has only 0 as eigenvalues
positive_passages.docid: 10001
positive_passages.text: Prove that the only eigenvalue of a nilpotent operator is 0?
negative_passages.docid: 120407
negative_passages.text: Is every noninvertible matrix a zero divisor?
negative_passages.docid: 88473
negative_passages.text: Proof that the trace of a matrix is the sum of its eigenvalues
negative_passages.docid: 121987
negative_passages.text: Direct proof that nilpotent matrix has zero trace
negative_passages.docid: 16439
negative_passages.text: What are the eigenvalues of matrix that have all elements equal 1?
negative_passages.docid: 60663
negative_passages.text: Let $\rho$ f.d. rep of a nilpotent Lie algebra such that $\rm{det} \rho(X) = 0$, $\forall X$. Then $\exists v \neq 0$: $\rho(X)v = 0, \forall X$.
negative_passages.docid: 125569
negative_passages.text: Prove that the eigenvalues of a real symmetric matrix are real
negative_passages.docid: 130268
negative_passages.text: How to prove that a nilpotent matrix is not invertible?
negative_passages.docid: 19649
negative_passages.text: A question about the proof of "a symmetric matrix has real eigenvalues".
negative_passages.docid: 70455
negative_passages.text: Why are all nonzero eigenvalues of the skew-symmetric real matrices pure imaginary?
negative_passages.docid: 14320
negative_passages.text: How to prove that eigenvectors from different eigenvalues are linearly independent
negative_passages.docid: 128043
negative_passages.text: $A^n=0$ for $A$ nilpotent without the use of minimal polynomial
negative_passages.docid: 52208
negative_passages.text: Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
negative_passages.docid: 41932
negative_passages.text: Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
negative_passages.docid: 33448
negative_passages.text: Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
negative_passages.docid: 7034
negative_passages.text: Prove that $A+I$ is invertible if $A$ is nilpotent
negative_passages.docid: 72046
negative_passages.text: Prove all eigenvalues of $A^*A$ are non-negative