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Jul
23
revised When does $n$-dimensional algebra have $m$-dimensional faithful representation?
edited title
Jul
21
reviewed Reject suggested edit on Set and cardinality injection and surjection proof
Jul
19
reviewed Reject suggested edit on “Advective”, “diffusive”, “dispersive”, and related terms in the realm of PDEs
Jul
18
comment Dimension of a weight space which is of weight $0$.
This is false without further assumptions on $V$. Even if $V$ is irreducible it is still wrong, e.g. the adjoint rep of $\mathfrak{sl}_3(\mathbb{C})$ has zero weight space of dimension two, spanned by the CSA.
Jul
17
comment Does this arithmetic operation have a name
I mean that it respects the product operations, so a monoid morphism if you like. But you can upgrade to an isomorphism of fields if you use Henry's addition: as fields, $(R,\cdot,+)\cong(R,\times,add)$
Jul
17
comment Does this arithmetic operation have a name
This is a shifted version of ordinary multiplication. Consider the map $f(x)=1-x$, which is a morphism from the reals with ordinary multiplication to the reals with $\times$
Jul
15
comment Representations of group algebra and its centre
I deleted my comment because of a typo. The problem is that irreps of the centre of $\mathbb{C}G$ are not usually reps of G themselves - what would the action of G be? Indeed all irreps of a commutative algebra over the complex numbers are 1D, whereas nonabelian G have larger irreps. So the question needs to be clarified a bit. There is a bijection between irreps here...
Jul
11
comment Dealing with Fatigue
This question appears to be off-topic because it is not about math
Jun
30
comment In Group theory proofs what is meant by “well defined”
What is the object $\phi$ about which you could ask the question "is this well-defined"? If it is a function, you are begging the question. If it is a relation, then notation like $\phi(g)$ doesn't seem to make sense. So maybe it is something else -- could you clarify what kind of object your definition of well-definedness applies to?
Jun
25
reviewed Leave Open Prove that if $A - A^2 = I$ then $A$ has no real eigenvalues
Jun
25
reviewed Close Quick check on function composition notation
Jun
22
revised Showing the following rings are isomorphic
fix typo in title
Jun
21
reviewed Approve suggested edit on How do you integrate the reciprocal of square root of cosine?
Jun
17
reviewed Approve suggested edit on Linear algebra: determining if something is an inner product space
Jun
14
comment Happily Married
en.wikipedia.org/wiki/Hall%27s_marriage_theorem
Jun
14
comment What are the formulas for the number of vertices, edges, faces, cells, 4-faces, …, $n$-faces, of convex regular polytopes in $n \geq 5$ dimensions?
en.wikipedia.org/wiki/Hypercube, en.wikipedia.org/wiki/Simplex, en.wikipedia.org/wiki/Orthoplex answer all your questions.
Jun
14
reviewed Approve suggested edit on Minimal polynomial of diagonalizable matrix
Jun
14
comment Complete induction - is my proof valid?
It's the right idea, but not quite expressed correctly: what are $c,d$ supposed to be when first introduced? You should say that if $n+1$ is prime you're done, and if not you can factor it as $n+1=cd$ with $c,d<n+1$. Then you can apply the inductive hypothesis to $c$ and $d$.
Jun
13
reviewed Reject suggested edit on Markov/Chebyshev's inequality Problems
Jun
12
reviewed Approve suggested edit on Prove by induction that $(n+1)^2 + (n+2)^2 + … + (2n)^2 = \frac{n(2n+1)(7n+1)}{6}$