Characteristic Polynomial

The characteristic polynomial is a mathematical expression associated with a square matrix that encodes essential information about its properties, especially its eigenvalues. It is derived from the matrix itself and helps identify these eigenvalues by solving a related polynomial equation. In practical terms, the characteristic polynomial acts like a fingerprint for the matrix, revealing critical insights into its behavior, such as how it scales or transforms space when applied as a linear transformation. This concept is fundamental in areas like engineering, physics, and computer science, where understanding transformations and systems is essential.