query: Prove: $\det(A)=0$ where $A\in M^{(2k+1)\times(2k+1)}(\mathbb{R})$ is anti-symmetric
positive_passages.docid: 150715
positive_passages.text: Prove that the determinant of skew-symmetric matrices of odd order is zero
negative_passages.docid: 78224
negative_passages.text: Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
negative_passages.docid: 52928
negative_passages.text: If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
negative_passages.docid: 122951
negative_passages.text: If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?
negative_passages.docid: 129647
negative_passages.text: $A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
negative_passages.docid: 29568
negative_passages.text: Prove that the determinant of $ A^{-1} = \frac{1}{det(A)} $- Linear Algebra
negative_passages.docid: 110200
negative_passages.text: Determinant of a Special Symmetric Matrix
negative_passages.docid: 33891
negative_passages.text: If $\mathbf A$ and $\mathbf B$ are Hermitian, when does $\det(\mathbf A-\lambda\mathbf B)=0$ have only real roots?
negative_passages.docid: 143793
negative_passages.text: If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite
negative_passages.docid: 84522
negative_passages.text: A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix
negative_passages.docid: 99600
negative_passages.text: Show that a 2x2 matrix A is symmetric positive definite if and only if A is symmetric, trace(A) > 0 and det(A) > 0
negative_passages.docid: 38378
negative_passages.text: $M= \{ A \in Mat_{2 \times 2}{\mathbb{R}}| \det(A)=1 \}$ is homeomorphic to $S^{1} \times \mathbb{R}^{2}$
negative_passages.docid: 22222
negative_passages.text: Properties of zero-diagonal symmetric matrices
negative_passages.docid: 55232
negative_passages.text: Show that $g\circ f\equiv 0$ implies $\det Df\equiv 0$, where $g(x_1,...,x_n)=x_1^5+...+x_n^5$
negative_passages.docid: 70381
negative_passages.text: Find the determinant of a symmetric matrix
negative_passages.docid: 20920
negative_passages.text: Determinant of a block skew-symmetric matrix
negative_passages.docid: 75855
negative_passages.text: Show that $\det{(A + sxy^*)}$ is linear in $s$