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....