There is exactly one group $G$ of four elements, say $G = \{e, a, b, c\}$ satisfying the additional property that $xx = e$ for every $x \in G$. Complete t...

Consider the following generating formula: $$\frac{t}{e^t-1}=\sum_{n=1}^{\infty} B_n \frac{t^n}{n!}$$ There is some intuitive explanation about it? I want...

I have a matrix $M$ and I would like to find two vectors $u$ and $v$, that minimize $$ \sum_{i,j} (M_{i,j}-u_iv_j)^2 $$ How can I do this (numerically)? A...

I want to read about famous Indian mathematicians (for example, Ramanujan, Aryabhatta, etc.), their biographies and their research contributions. Please s...

I am reading about right-inverse and left-inverse matrices. According to theory if a matrix $A_{m\times n}(\mathbb{R})$ is full row rank, then it has a ri...

I have some problems with this In response to an attack of 10 missiles, 500 antiballistic missiles are launched. The missile targets of the antiballistic ...

How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?

I am having trouble with notations like 1 cm$^{-3}$, especially since I am converting them between compound units. Is there a way to express 1 cmcm$^{-3}$...

I got this result when I threw a set of 10 dice (btw. for the first with this set): What is a probability of getting 6 identical numbers (any) with 10 dic...

I am working on a past Algebra exam paper and have come across a problem which requires me to write the linear operator associated to a given matrix $M$ i...