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Results tagged with linear-algebra
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user 367
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
3
votes
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answer
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spurious torsion under compositions of linear maps
Say we have a PID $R$, integers $1 \leq a \leq b$, and $R$-homomorphisms $R^a \stackrel f\to R^b \stackrel g\to R^a$ with $g \circ f$ of full rank.
For $h = f, g, g \circ f$, let $c(h)$ be the charac …
- 735
0
votes
Accepted
spurious torsion under compositions of linear maps
Here is an obvious way to construct examples with $a=1,b=2$. By elementary divisor theory, with these numerics one always has $f=uf_0,g=vg_0$ with $c(f_0),c(g_0)=1$ for some $u,v \in R$, so it suffic …
- 735