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Jan
26
comment Category of $\textbf{Ring}$.
it's sometimes easier to have a convention that excludes slightly trivial or slightly pathological examples. Dummit and Foote just take a ring to mean something with a unit, they never deal with unit-less rings, and it's extra baggage to carry that around when you aren't using it.
Jan
26
comment Univariate and Matrix Representation of Affine Transformation
the map $\phi$ is implicit in what I'm doing, it's essentially a change-of-basis matrix. if you let $e_i$ be the canonical basis (a column with all 0s except on the i-th row, that's a 1) for $\mathbb{F}^n$, then $\phi : \mathbb{F}^n \to \mathbb{E}^n$ by $e_i \mapsto \{\text{some expression in the t basis I gave}\}$ then it'll do the trick.
Jan
25
comment Univariate and Matrix Representation of Affine Transformation
I'm not 100% sure I'm correct on the last step, but hopefully you see the idea now? :)
Jan
25
revised Univariate and Matrix Representation of Affine Transformation
expanding a lot
Jan
25
comment Application of Category Theory
you might look at these questions: math.stackexchange.com/questions/312605/… and mathoverflow.net/questions/19325/… (heavier maths there)
Jan
25
revised Univariate and Matrix Representation of Affine Transformation
missing a key detail about the finite field.
Jan
25
answered Univariate and Matrix Representation of Affine Transformation
Jan
25
suggested approved edit on Univariate and Matrix Representation of Affine Transformation
Jan
25
revised Univariate and Matrix Representation of Affine Transformation
grammar, correction of definitions.
Jan
25
suggested approved edit on Univariate and Matrix Representation of Affine Transformation
Jan
23
asked kernel of maps associated to the root of an irreducible polynomial
Jan
18
revised Prove $\ker {T^k} \cap {\mathop{\rm Im}\nolimits} {T^k} = \{ 0\}$
correct def of Im
Jan
18
suggested approved edit on Prove $\ker {T^k} \cap {\mathop{\rm Im}\nolimits} {T^k} = \{ 0\}$
Jan
15
revised when is a ring a free module over a subring?
edited tags
Jan
15
revised when is a ring a free module over a subring?
added 3 characters in body
Jan
15
awarded  Critic
Jan
14
asked when is a ring a free module over a subring?
Jan
14
comment Most efficient way to find distinct complementary subspaces over a finite field
is there an algorithmically efficient way to complete $\{v_{n-k+1},\ldots, v_n\}$ to a basis $\{v_1,\ldots,v_n\}$. Your description solves the problem wonderfully (though I no longer need such a solution!), but I might be too silly to see an way to complete the basis.
Jan
14
revised Most efficient way to find distinct complementary subspaces over a finite field
fixed error in denom.
Jan
14
comment Most efficient way to find distinct complementary subspaces over a finite field
you're correct, my bad. changed question.