Eigenvalues and eigenvectors have varying physical significance depending on their application, particularly in fields like engineering and signal processing. The physical meaning of an eigenvector is tied to the context of the matrix it originates from, while eigenvalues are crucial for understanding system behaviors, such as frequency response. These concepts are essential in solving dynamic equations and can simplify complex mathematical manipulations. In signal processing, the physical significance of operations like multiplying a signal by a transfer function can be interpreted in terms of system response. Overall, the relevance of eigenvalues and eigenvectors is context-dependent, emphasizing their utility across different scientific domains.