Answer to Question #136985 in Discrete Mathematics for Rakibul

Question

Define the following terms with proper example:

a. Relatively prime integers
b. Hadamard Matrix

Answer 1

a. Two integers are relatively prime if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 11 and 12 are relatively prime, but 12 and 14 are not.

b. A Hadamrd matrix is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. For example the following matrix $A$ is a Hadamrd matrix because the scalar product of vector-rows $(1,1)$ and $(1,−1)$ is equal to zero, that is $(1,1)(1,-1)=1\cdot 1+1\cdot(-1)=0$.

$A=\left( \begin{array}{cc} 1 & 1\\ 1 & -1 \end{array}\right)$