query: Show that if all row-sums of a square matrix $A$ are equal to $0$, then $A$ is singular
positive_passages.docid: 18297
positive_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: 35897
negative_passages.text: Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
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: 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: 55031
negative_passages.text: Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
negative_passages.docid: 47012
negative_passages.text: When a 0-1-matrix with exactly two 1’s on each column and on each row is non-degenerated? [1]
negative_passages.docid: 31326
negative_passages.text: Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns
negative_passages.docid: 31116
negative_passages.text: Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
negative_passages.docid: 55820
negative_passages.text: If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$.
negative_passages.docid: 124095
negative_passages.text: $A$ is a real orthogonal matrix, prove that $ (I+A)^{-1}(I-A)$ is skew-symmetric
negative_passages.docid: 120687
negative_passages.text: If the sum of eigenvectors is an eigenvector, then they all correspond to the same eigenvalue
negative_passages.docid: 31149
negative_passages.text: Prove that matrix can be square of matrix with real entries
negative_passages.docid: 5616
negative_passages.text: How can I prove the IFF condition for this group of matrices?
negative_passages.docid: 69474
negative_passages.text: Orthogonal projections with $\sum P_i =I$, proving that $i\ne j \Rightarrow  P_{j}P_{i}=0$
negative_passages.docid: 51967
negative_passages.text: Prove that if the sum of each row of $A$ equals $s$, then $s$ is an eigenvalue of $A$.
negative_passages.docid: 65783
negative_passages.text: Proving: "The trace of an idempotent matrix equals the rank of the matrix"
negative_passages.docid: 14481
negative_passages.text: How do I show that the sum of residuals of OLS are always zero using matrices