In this article  we shall show that the characteristic polynomial of both $$AB$$ and $$BA$$ are the same, where $$A$$ and $$B$$ are $$n\times n$$ matrices over $$R$$, a ring with unity. Let $$\Phi_T\in R[\lambda]$$ denote the characteristic polynomial of $$T$$. Thus, we intend to show,...

Given a straight line $$l$$ and points $$A$$ and $$B$$ on the same side of it find the shortest path from $$A$$ to $$B$$ which touches $$l$$. Given a function $$f:\mathbb{Q}\rightarrow\mathbb{Q}$$ such that $$f(x+y)=f(x)+f(y)$$ Show that $$f(x)=xf(1)$$ for all $$x\in\mathbb{Q}$$. Thus, infer that for such a...

Professor Ambat Vijaykumar of CUSAT, Cochin releases a yearly brochure about information on mathematics that is useful to students and teachers in India alike. The 2016-17 version of the brochure can be found below. [pdf-embedder url="http://gonitsora.com/wp-content/uploads/2016/08/Mathematics_Information_Brochure_2016-1.pdf" title="Mathematics_Information_Brochure_2016"] If the file is not visible, then please click here....

The Abdus Salam International Centre for Theoretical Physics (ICTP) at Trieste, Italy awards the prestigious Dirac Medal and Prize every year. This year, it was awarded to Nathan Seiberg (Institute for Advanced Study, Princeton), Mikhail Shifman (University of Minnesota) and Arkady Vainshtein (University of Minnesota)...