query: Prove that $A$ is a singular matrix if and only if zero is an eigenvalue (of $A$)
positive_passages.docid: 52208
positive_passages.text: Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
negative_passages.docid: 63260
negative_passages.text: Matrices whose Linear Combinations are All Singular
negative_passages.docid: 5322
negative_passages.text: Let $A$ be a complex matrix such that $A^n = I$, show that $A$ is diagonalisable.
negative_passages.docid: 112701
negative_passages.text: Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
negative_passages.docid: 111550
negative_passages.text: Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
negative_passages.docid: 128453
negative_passages.text: If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
negative_passages.docid: 29788
negative_passages.text: Eigenvalues of a matrix whose square equals its transpose
negative_passages.docid: 121982
negative_passages.text: Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
negative_passages.docid: 81176
negative_passages.text: A normal matrix with real eigenvalues is Hermitian
negative_passages.docid: 116539
negative_passages.text: Eigenvalues of matrix satisfying $A^2 = A$
negative_passages.docid: 97733
negative_passages.text: Can it be determined that the sum of the diagonal entries, of matrix A, equals the sum of eigenvalues of A
negative_passages.docid: 14320
negative_passages.text: How to prove that eigenvectors from different eigenvalues are linearly independent
negative_passages.docid: 118283
negative_passages.text: Show that if $A^{n}=I$ then $A$ is diagonalizable.
negative_passages.docid: 18297
negative_passages.text: Suppose that each of the row sums of an $n\times n$ matrix $A$ is equal to zero. Show that $A$ must be singular.
negative_passages.docid: 7457
negative_passages.text: Prove that $J^+AJ$ has positive eigenvalues
negative_passages.docid: 106288
negative_passages.text: Prove that the eigenvalues of a block matrix are the combined eigenvalues of its blocks
negative_passages.docid: 61274
negative_passages.text: If $AA^T$ is the zero matrix, then $A$ is the zero matrix