query: trace $0$ complex matrix is similar to a diagonal matrix having $0$'s in main diagonal
positive_passages.docid: 52928
positive_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: 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: 105141
negative_passages.text: $\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$
negative_passages.docid: 52621
negative_passages.text: Why is $\det(A - \lambda I)$ zero?
negative_passages.docid: 138605
negative_passages.text: Why `Chop` does not make the real part of machine complex numbers an exact zero?
negative_passages.docid: 79808
negative_passages.text: Prove the representation of complex numbers is parallelogram
negative_passages.docid: 105727
negative_passages.text: Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$
negative_passages.docid: 75104
negative_passages.text: Existence of some type matrix
negative_passages.docid: 114250
negative_passages.text: If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
negative_passages.docid: 48658
negative_passages.text: Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
negative_passages.docid: 32064
negative_passages.text: Zero-dimensional matrices
negative_passages.docid: 35247
negative_passages.text: The characteristic and minimal polynomial of a companion matrix
negative_passages.docid: 57070
negative_passages.text: Dimensionality of null space when Trace is Zero
negative_passages.docid: 122951
negative_passages.text: If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?
negative_passages.docid: 58595
negative_passages.text: Existence of a G-invariant matrix
negative_passages.docid: 24454
negative_passages.text: The relationship between the eigenvalues of matrices $XY$ and $YX$
negative_passages.docid: 7813
negative_passages.text: In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$