Characteristic Polynomial: Definition & Examples

This lecture covers the definition of the characteristic polynomial of a matrix, which is defined as the determinant of (A - tI), where A is the matrix and t is an indeterminate. Examples are provided to illustrate the calculation of the characteristic polynomial for different matrices. The lecture also discusses the concept of similarity between matrices and how similar matrices have the same characteristic polynomial. Additionally, it explains the characteristic polynomial of a linear transformation in a finite-dimensional vector space, emphasizing the importance of understanding this concept in linear algebra.