query: $A\in \mathrm{Mat}_n(\mathbb{Z})$ is the matrix representing $f$. Show that if $\mathrm{Coker}(f)$ is finite, then $|\det A|=|\mathrm{Coker}(f)|$.
positive_passages.docid: 145339
positive_passages.text: Index of the subgroup $\operatorname{Im}(f)$
negative_passages.docid: 52750
negative_passages.text: Prove that $f^\ast\omega=\det f \cdot \omega$
negative_passages.docid: 98816
negative_passages.text: How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
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: 142640
negative_passages.text: Prove determinant of a matrix $=\prod_{j<i}(a_i-a_j)$
negative_passages.docid: 87451
negative_passages.text: Construction of matrices under ZFC axioms
negative_passages.docid: 37249
negative_passages.text: Suppose $A$ is a 4x4 matrix such that $\det(A)=\frac{1}{64}$
negative_passages.docid: 23224
negative_passages.text: $\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$
negative_passages.docid: 29545
negative_passages.text: $[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
negative_passages.docid: 3296
negative_passages.text: Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
negative_passages.docid: 81181
negative_passages.text: Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
negative_passages.docid: 63119
negative_passages.text: Let $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$. Prove $\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$.
negative_passages.docid: 134442
negative_passages.text: Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?
negative_passages.docid: 89553
negative_passages.text: proof that every finite matrix has an annihilating polynomial
negative_passages.docid: 4295
negative_passages.text: Let $N$, $K$ be sub-modules of $M$ with $I=\mathrm{Ann}(N)$, $J=\mathrm{Ann}(K)$. Show $I+J$ is a proper subset of $\mathrm{Ann}(N \cap K)$.
negative_passages.docid: 59134
negative_passages.text: Proving idempotent elements in $\mathbb{Z}_n$
negative_passages.docid: 145104
negative_passages.text: $T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$