The Cayley-Hamilton Theorem states that every square matrix satisfies its own characteristic equation. This means that if you substitute the matrix itself into its own characteristic equation, the result will always be equal to the zero matrix.
Arthur Cayley and William Hamilton were two mathematicians who independently discovered and proved the Cayley-Hamilton Theorem in the mid-19th century.
The Cayley-Hamilton Theorem is a fundamental result in linear algebra and is used in various applications, including solving systems of linear equations, finding eigenvalues and eigenvectors, and diagonalizing matrices.
No, the Cayley-Hamilton Theorem only applies to square matrices. However, there are similar theorems that apply to non-square matrices, such as the Jordan Canonical Form Theorem.
The Cayley-Hamilton Theorem has applications in many fields, including physics, engineering, and computer science. It is used in control theory, signal processing, and image processing, among others.