query: $A$ and $B$ be two orthogonal matrices with $|A|+|B|=0$. Then prove that $(A+B)$ is singular
positive_passages.docid: 109573
positive_passages.text: Is sum of two orthogonal matrices singular?
negative_passages.docid: 158845
negative_passages.text: Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$.
negative_passages.docid: 59397
negative_passages.text: Eigenvalues of $AB$ and $BA$ where $A$ and $B$ are square matrices
negative_passages.docid: 73677
negative_passages.text: If the matrix $A^3 = 0$, is $A$ singular?
negative_passages.docid: 41932
negative_passages.text: Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
negative_passages.docid: 75066
negative_passages.text: If the product of two square matrices is invertible, then both matrices are invertible
negative_passages.docid: 24809
negative_passages.text: For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$?
negative_passages.docid: 110381
negative_passages.text: Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 69497
negative_passages.text: Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
negative_passages.docid: 29055
negative_passages.text: How to prove that $c_0I+c_1A+..+C_nA^n$ is singular if $(v,Av,A^2v,...,A^nv)$ is linearly dependent, $v \in \mathbb{F^n}$ and $A_{n \times n}$?
negative_passages.docid: 35625
negative_passages.text: Direct sum of orthogonal subspaces
negative_passages.docid: 102817
negative_passages.text: $A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
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: 18012
negative_passages.text: Eigenvectors of real symmetric matrices are orthogonal
negative_passages.docid: 14189
negative_passages.text: If $(I-A)(I+A)^{-1}$ is orthogonal then prove that A is skew symmetric.
negative_passages.docid: 6960
negative_passages.text: Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal