Find the Domain aij=-aij

Problem

(a_i*j)=−(a_j*i)

Solution

1. Identify the definition of the given equation. The condition (a_i*j)=−(a_j*i) for all indices i and j defines a skew-symmetric (or anti-symmetric) matrix.

2. Determine the constraints on the indices. For a matrix A with entries (a_i*j) the indices i and j represent the row and column positions respectively.

3. Analyze the diagonal elements. When i=j the equation becomes (a_i*i)=−(a_i*i) which implies 2*(a_i*i)=0 or (a_i*i)=0

4. Define the domain of the indices. In the context of an n×n square matrix, the domain for both i and j is the set of integers from 1 to n

Final Answer

i,j∈{1,2,…,n}

Want more problems? Check here!