Cayley – hamiltion theorem By Sunny

Cayley-Hamilton Theorem

1. Cayley –Hamilton Theorem Presented By Md . Rabius Sani Biplob Sarker Fahmida Hossain Bappy Das Nila

2. About Cayley -Hamilton Arthur Cayley :(16 August 1821 – 26 January 1895) was a British Mathematician.

3. About Sir William Rowan Hamilton Sir William Rowan Hamilton: (3–4 August 1805 – 2 September 1865) was an Irish physicist, astronomy, and mathematician

4. Cayley-Hamilton Theorem The Cayley - Hamilton Theorem states that a square n*n matrix A satisfies own characteristic equation. Thus, we can express A n in terms of a finite set of lower powers of A. This fact leads to a simple way of calculating the value of a function evaluated at the matrix A is: f( λ )= A is λ n + a 1 λ n-1 + a 2 λ n-2 +…………+ a n-1 λ +a n =0 Where I is the nth order unit matrix and 0 is the nth order zero matrix .

5. Proof The characteristic equation for the matrix A is | λ I-A|=0 which can be written as A n + a 1 A n-1 + a 2 A n-2 +…………+a n-1 A+a n I=0

6. Example of Cayley – Hamilton Theorem

7. Cayley - H amilton theorem is useful to find 1.Inverse & power of matrix 2.only inverse of matrix. 3.only power of matrix.

8. Uses of Cayley-Hamilton Theorem in EEE The Cayley - Hamilton theorem and its generalizations have been used in control systems, electrical circuits , systems with delays, singular systems . specially in DC circuit

9. Thank To All..