query: Is $\det(I+M\bar{M})\geq 0$ for any complex square matrix $M$?
positive_passages.docid: 144898
positive_passages.text: Let $A$ be complex matrix and $x$ be eigenvalue of $A\overline{A}$. Algebraic multiplicity of $x$ is even.
negative_passages.docid: 1865
negative_passages.text: Sub-determinants of an orthogonal matrix
negative_passages.docid: 7205
negative_passages.text: Find the determinant of $A + I$, where $A$ is a real matrix such that $AA^{\top}=I$ and $\det A<0$.
negative_passages.docid: 125348
negative_passages.text: Does $\det(A + B) = \det(A) + \det(B)$ hold?
negative_passages.docid: 84341
negative_passages.text: Can the determinant of a matrix can be made $0$?
negative_passages.docid: 23847
negative_passages.text: Determinant of a matrix whose $(i,j)$th element is $|i-j|$?
negative_passages.docid: 106619
negative_passages.text: Determinant of matrix
negative_passages.docid: 60900
negative_passages.text: If $A^2=-I$, Prove that $\det{A}=1$
negative_passages.docid: 51834
negative_passages.text: Positivity of a determinant
negative_passages.docid: 38550
negative_passages.text: 2x2 matrices with sum of diagonal entries equal zero
negative_passages.docid: 137422
negative_passages.text: $\mathrm{card}(\mathbb{Z}^n/M\mathbb{Z}^n) = |\det(M)|$?
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: 7384
negative_passages.text: How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
negative_passages.docid: 39256
negative_passages.text: Finding $\det(I+A^{100})$ where $A\in M_3(R)$ and eigenvalues of $A$ are $\{-1,0,1\}$
negative_passages.docid: 127799
negative_passages.text: Eigenvalues of symmetric matrices are real without (!) complex numbers
negative_passages.docid: 121358
negative_passages.text: What is the exact relation between a full rank matrix and its determinant?
negative_passages.docid: 81818
negative_passages.text: Prove or disprove : $\det(A^k + B^k) \geq 0$