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Mathematics
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Suman Kundu's user avatar
Suman Kundu's user avatar
Suman Kundu
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16
Suppose $A,B\in M_n(\mathbb{C})$ such that $AB-BA=A $ . Prove that $A$ is not invertible .
May 28, 2017
16
$f(x)=ax+b$ for some $a,b\in\mathbb{Q}$ if $f(\mathbb{Q})\subset\mathbb{Q}$ and $f(\mathbb{R-Q})\subseteq \mathbb{R}-\mathbb{Q}$
Mar 25, 2017
11
Reference request for CMI M.Sc entrance exam
Jun 4, 2017
11
A vector space is finite dimensional if all of its proper subspaces are finite dimensional
Apr 4, 2017
9
Does there exist a continuous f ,integration of $\int_{0}^{1} x^n f(x)= 1$ for all $n$
Feb 16, 2017
8
Let $A$ be a symmetric matrix of order $n$ and $A^2=0$ . Is it necessarily true that $A=0$
Apr 17, 2017
6
Suppose that poynomial $x^4+x+1$ has multiple roots over a field of characteristic $p$ . What are the possible values of $p$
Apr 15, 2017
5
5 boys and 3 girls are to be arranged such that only one girl has a boy adjacent to her . Find the number such arrangement
May 16, 2017
5
Prove that the largest number of $1$'s in the $n\times n$ invertible matrix $A$ with entries $0$ or $1$ is $n^2-n+1$
Apr 9, 2017
5
$p$ the smallest prime divisor of $|G|$ , $x\in G$ an element of order $p$ . Suppose $h\in G$ such that $hxh^{-1}=x^{10} $ . Show that $p=3 $ .
Apr 25, 2017