Devendra Singh Rana
  • Member for 4 years, 11 months
  • Last seen this week
  • India
1 answers
1 votes
29 views
How to find reflection of $(a,b)$ along $y=x, y = -x$
0 votes

Well, you can just use Basic Linear Algebra for instance just write the matrix of the transformation(Reflection in this case) with a usual basis in both the cases, then it will be very clear to you ...

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3 answers
3 votes
5k views
Types of singularities, why is this an essential singularity
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Well! As far as Complex exponential is concerned $e^\infty$ is not actually $\infty$ it is not defined to be precise. While understanding types of singularities you should also learn them by their ...

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4 answers
7 votes
226 views
Is $\frac 10 = \infty$?
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I have always known infinity as a concept not as a no. Dealing with infinity the way we deal with no. Is wrong ,we can't really do that. 1/0 is not equal to infinity just because it's a pattern ...

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3 answers
-2 votes
406 views
How to construct $F_2[x]/(x^3+x^2+1)$ quotient ring and check whether it is a field?
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Yes! If p(x) is irreducible then the ideal it generates will be a maximal ideal in F[x] where F is a field. And we have a well known result that R/I is a field iff I is maximal . hence the result ...

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2 answers
0 votes
46 views
Linear algebra Matrix-vector multiplication, transformation
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I think what you have done wrong is that , the vectors you have choosen are needed to be written as a column vector not as a row vector.

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5 answers
1 votes
1k views
Prove: $(a^{-1})^{-1}=a$ Over A Field
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Since a has an inverse then we have $$a•a^{-1}=a^{-1}•a=1$$ Then we just replace a by b to get $$ b•a^{-1}=a^{-1}•b=1$$ Which gives us that b is actually the inverse of $a^{-1}$ ...

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3 answers
0 votes
47 views
Convergence of $\sum_{n=1}^{\infty}|x_n+y_n|$
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It is quite clear , you can just use the triangle's inequality and then the comparison test to prove your result.

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2 answers
1 votes
561 views
What eigenvectors can be used to find the Jordan canonical form?
0 votes

Any two generalize eign vector should work. You can. Find them just by solving (A-λI)X1=X, (A-λI)X2=X1, where X is the eigenvector . And X1 X2 are corresponding generalize eign vectors..

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2 answers
2 votes
2k views
complete vector spaces intuition
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Completeness is all about convergence of cauchy sequences inside the space . To study about the convergence to sequence in a space one must know the topological structure of that space so that one can ...

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3 answers
1 votes
656 views
Dihedral Groups; what exactly are the elements of the set?
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Definition 1 clearly tells you that r is the rotation of a regular n-gon by 2π/n radians which is a single element . To understand it precisely you draw a square ,mark the edges and then try to ...

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2 answers
1 votes
264 views
Is the complex plane open in the extended complex plane?
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Yes then you can prove it by contradiction, suppose C is not an open subset of C∪{∞} then there exist some point say x in C such that any open ball of radius r around x is not completely inside of C ...

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