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Aug
23
comment Sum of largest two angles
You know the possible sizes of an obtuse angle if it's divisible by 9; you know the sum of the angles of a 7-sided polygon; can you work out something about the sizes of the individual angles? You're expected to at least have a go at a problem you post here, not just dump it here without putting any thought into it yourself.
Aug
23
comment The matrix of a linear transformation
If you understand it now, you can write it up and post it as an answer. It's good practice.
Aug
23
comment The matrix of a linear transformation
Look: $T(1,0,-1)=(1,-3)$. But $(1,-3)=(-4)(0,1)+(1)(1,1)$, so what is $(1,-3)$ with regard to the standard basis is $(-4,1)$ with regard to the given basis, and if you want $Av=T(v)$ then you have to use that $(-4,1)$, not $(1,-3)$.
Aug
23
comment continuous and discontinuous functions
Tom, you're still not telling us what you mean by "have infinite values". Maybe you mean, "takes on infinitely many different values". Or maybe you mean, "take on every real value between its maximum and its minimum". Or maybe you mean, "only takes on the value infinity". Or maybe you mean something else. Please try again.
Aug
23
comment Stirling number
Have you tried calculating the first few to see what they look like?
Aug
23
comment complex conjugate of exponent
If you can write $f=u+iv$ where $u$ and $v$ are real functions, the conjugate should just be $(1-ce^{-iu-v})^N$.
Aug
23
comment The matrix of a linear transformation
Because the definition of the transformation matrix is the matrix $A$ such that $Av=T(v)$ when $v$ is expressed in the basis of the domain and $Tv$ is expressed in the basis of the codomain.
Aug
23
revised is the next function continuous at (0,0) ? + theoretical question
typos in title
Aug
23
comment is the next function continuous at (0,0) ? + theoretical question
The rule of thumb would appear to be false for $x/(x^2+1)$.
Aug
23
revised The matrix of a linear transformation
edited tags
Aug
23
comment The matrix of a linear transformation
But you have to take the result vectors and express them with regard to the 2nd basis.
Aug
23
comment continuous and discontinuous functions
Why should I???
Aug
23
comment How can the set $\{1\}$ be in the co-finite topology?
Somewhere it ought to say that $X$ is a finite set; otherwise, most of those sets don't have a finite complement.
Aug
23
comment Quadratic Diophantine Primality Testing
It seems to me that to determine whether $x^2+y^2=Q$ has a solution, one needs to factor $Q$ (as finding the residues mod 4 of the prime factors seems to be as hard as factoring), and no one knows how to factor in polynomial time.
Aug
23
comment Quadratic Diophantine Primality Testing
When you write, "there do not exist integers $a_1,\dots,a_5$ such that....", do you mean, "there do not exist integers $x_1,x_2$ such that...."?
Aug
23
comment Find the homogeneous polynomials whose set of values is closed under multiplication
All norm forms should work --- most of your examples are norm forms, or powers of norm forms. Any universal form will work, too (any form that represents all integers, or all positive integers).
Aug
23
comment Linear transformation? Image?
I haven't checked to see whether $M$ is right, but, if it is, then your eigenvectors are now correct. The eigenspace is not 2; the eigenspace is a vector space, whereas 2 is a number. But the dimension of the eigenspace is 2.
Aug
23
answered One well-known property of resultant
Aug
23
comment One well-known property of resultant
If you start from the Sylvester determinant, it's stated as Theorem 1.6 in www2.math.uu.se/~svante/papers/sjN5.pdf and proved a few pages later.
Aug
23
comment One well-known property of resultant
You can take that formula as the definition of the resultant. What definition of the resultant are you starting from?