Linear Algebra

The Cayley-Hamilton theorem is about the characteristic equation of a square matrix. Using this theorem one can find the inverse of a matrix, the integral power of a matrix, and many more. In this post, we will study this theorem along with some applications. Cayley-Hamilton Theorem Statement Statement: Every square matrix satisfies its own characteristic … Read more

The characteristic equation of a matrix is an important tool to study a matrix. Using this equation, we can find the eigenvalue with its corresponding eigenvectors to analyse a matrix. In this post, we will learn about the characteristic equation of a matrix. Definition Let A be an n×n matrix over a field F. The … Read more