<p>When introducing architectural innovations into existing systems, engineers aim to choose design modifications that would cause the least amount of architectural change to the existing system while achieving the intended performance gains. This article presents a new method to estimate the degree of architectural change based upon the mathematics of matrix eigenvector rotation, where such a matrix represents the architecture of the system. The degree of eigenvector rotation assesses the sensitivity of a system architecture to introduced innovations, which are modeled as perturbations. The article evaluates the validity of the method using synthetic product architectures, a comparison to a previously published approach that also uses eigenvalue analysis, and a case study on a real-world industrial system. The evaluations demonstrated that eigenvector rotation is an effective mathematical construct to indicate the degree of architectural change an innovation may produce when local changes can trigger global effects or when architectural innovations involve system-wide changes.</p>