Thompson's Theorem

Thompson's Theorem states that in a matrix with specific properties, such as being Hermitian (equal to its own conjugate transpose), the largest value you can get when applying a linear functional (like a weighted sum of the matrix's entries) is equal to its largest eigenvalue. In simpler terms, it links the maximum output of a weighted sum across all possible vectors to the most dominant characteristic (the largest eigenvalue) of the matrix. This helps understand how the matrix behaves and how its most significant direction influences its overall impact.