Caley-Hamilton Theorem

Caley-Hamilton Theorem

To  understand  Caley-Hamilton theorem you have to know about characteristic polynomial.

Characteristic Polynomial

If A is a square matrix of of size n * n, and I is identity matrix of the same size as A. Then determinant |A-λI| will result in an equation of the form.

Caley-Hamilton TheoremWhich is called characteristic equation of matrix A
The root of characteristic equation are called eigen values of matrix A.

Caley-Hamilton theorem

The theorem states that characteristic equation of a square matrix is satisfies by itself.

i.e.

Caley-Hamilton Theorem

I will explain it  using a 2 × 2 matrix

Caley-Hamilton Theorem

Conclusion-

Theorem is very important result from linear algebra. Which is a lot of applications in matrix and polynomial related problem. In this post, I have explained the theorem in a very concise  form. Hope it will help you for further study of linear algebra and, further, you will also apply somewhere.

 

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