Cayley-Hamilton theorem

The Cayley–Hamilton theorem states that every square matrix satisfies:

• Its minimal polynomial
  

• Its eigenvalues
  

• Its characteristic polynomial

• Its determinant

If A is a 2X2 matrix, then Cayley–Hamilton theorem gives a relation involving:

• A³ and lower powers

• A² and lower powers

• A⁴ and lower powers

• Only A

By Cayley–Hamilton theorem, the matrix equation is:

• 
• 
• 
• 

By Cayley–Hamilton theorem, which relation holds?

• 
• 
• 
• 

In control systems, Cayley–Hamilton theorem helps in computing the state-transition matrix e^At because:

• It avoids eigenvalue computation
  

• It reduces system order

• It expresses higher powers of A in terms of lower powers

• It diagonalizes the system automatically