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0
votes
0answers
396 views
How do I get this matrix in Smith Normal Form? And, is Smith Normal Form unique?
As part of a larger problem, I want to compute the Smith Normal Form of $xI-B$ over $\mathbb{Q}[x]$ where
$$
B=\begin{pmatrix} 5 & 2 & -8 & -8 \\ -6 & -3 & 8 & 8 \\ -3 & ...
3
votes
1answer
98 views
Do a matrix and its transpose have the same invariant factors over a PID?
I suspect this is true since it holds in the case over a field. But suppose $A\in M_{m\times n}(R)$ where $R$ is a PID. Does it still hold that $A$ and $A^{T}$ have the same invariant factors?
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