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location Fiji
age 37
visits member for 2 years, 4 months
seen 35 mins ago

I'm a lecturer of mathematics at the University of the South Pacific. My research interests are in algebraic topology and metric geometry.


Aug
25
comment If $G/K\cong H/K$ must $G\cong H$?
You are welcome and no, not in any profitable way.
Aug
25
answered If $G/K\cong H/K$ must $G\cong H$?
Aug
25
answered How to make the Symmetric Distance a metric?
Aug
25
answered Can only one ordered pair be a relation?
Aug
24
comment Uniqueness of the direct product decomposition of finite groups
@Timbuc you are right. I was sure OP was talking about abelian groups.
Aug
24
answered Vector Spaces: canonical basis for the usual vector spaces
Aug
24
awarded  Talkative
Aug
24
answered Domain and Function Relationship
Aug
24
comment Why do we study representations of groups but not fields?
@MarcvanLeeuwen Yes! The thing is to have a useful representation theory and that usually comes from considering particularly nice (i.e., geometrically rich) structures). Of course, any group can be represented as a group of permutations on a set, but a set is not terribly rich. Similarly for representations of rings, as you say, just having an abelian group does not yield terribly interesting stuff. Having a vector space there helps.
Aug
24
answered Why do we study representations of groups but not fields?
Aug
24
answered Proof Regarding Diagonalizability, Eigenspace and Multiplicity
Aug
24
comment Definition of characteristic polynomial
you need to argue that matrices related by change of base have the same determinant, otherwise what you defined above may be basis dependent. Besides, I don't think this is what OP asked.
Aug
24
comment Definition of characteristic polynomial
@Phrohlych the one-to-one correspondence up to change of basis is not the issue here. Firstly, it is irrelevant that the correspondence is 1-1. Secondly, you need much more than a bijective correspondence. You need to know that the determinant is multiplicative and you need to know how change of base affects the matrix.
Aug
24
answered Definition of characteristic polynomial
Aug
20
comment Is $(\mathbb{R},\tau_B)$ a separable space?
Hint: What is the closure of the rationals?
Aug
19
comment Why are all convergent sequences necessarily Cauchy?
not all the elements in the sequences need to get close to anything. Only from some $N$ onwards. In general, convergence and Cauchyness are unaffected by changing, or discarding, finitely many elements in the sequence, no matter how large the number of changes you make.
Aug
19
comment interval of convergence of $e^x$
what are you having difficulty with?
Aug
19
answered Why are all convergent sequences necessarily Cauchy?
Aug
19
comment The category of theorems and proofs
is your question how to define this category or are you looking for a mathematical study of this category?
Aug
17
revised Boundedness of continuous functions on compact sets
edited body