Chebotarev's theorem for cyclic groups of order pqpq and an uncertainty principle

Key Points

• Chebotarev's theorem confirms that every square submatrix is nonsingular, revealing structural properties of matrices.
• The study proves the theorem for principal submatrices when the group order is the product of two distinct primes.
• An uncertainty principle for cyclic groups of order pq emerges, linking matrix theory to group theory.
• Applications of the theorem provide deep insights into the behavior of submatrices in algebraic structures.