Cayley Hamilton Thm

The Cayley-Hamilton theorem states that:

• Every square matrix is diagonalizable
  

• Every square matrix satisfies its own characteristic equation

• The determinant of a matrix is always positive

• The trace of a matrix equals the sum of eigenvalues

In electrical circuit analysis, Cayley-Hamilton theorem is useful for:

• Finding eigenvectors
  

• Inverting admittance or impedance matrices

• Determining resonance frequency

• Simplifying Bode plots

• 
• 
• 
• 

In control systems (ECE), Cayley-Hamilton theorem helps in:

• Frequency scaling
  

• Solving state-space equations

• Noise suppression

• Analog to digital conversion

Which of the following is a practical example where Cayley-Hamilton is applied in ECE?

• Phase Locked Loop (PLL) tuning
  

• Determining transition matrices in DSP

• Calculating duty cycle in PWM

• Spectrum analysis in SDR

The Cayley-Hamilton theorem is mainly applicable to:

• Diagonal matrices only
  

• Only real symmetric matrices

• All square matrices

• Only invertible matrices

Which of the following is needed to apply the Cayley-Hamilton theorem?

• Determinant of the matrix
  

• Trace of the matrix

• Characteristic polynomial of the matrix

• Rank of the matrix

Cayley-Hamilton theorem helps express higher powers of a matrix in terms of:

• Scalar values
  

• Lower-order powers of the same matrix

• Transposed matrices
  

What is the characteristic equation of a matrix AAA with eigenvalues 1, 2, and 3?

• 
• 
• 
• 

• 
• 
•