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Is there a known method to find a set of $\theta$ such that at least one eigenvalue of $A(\theta)$ is purely real?

Assume $A(\theta)$ is a real square matrix whose elements are linear functions of a real scalar $\theta$. I am interested in a general case (not assumeassuming $A$ is symmetric/positive-definite/etc.)

Is there a known method to find a set of $\theta$ such that at least one eigenvalue of $A(\theta)$ is purely real?

Assume $A(\theta)$ is a real square matrix whose elements are linear functions of a real scalar $\theta$. I am interested in a general case (not assume $A$ is symmetric/positive-definite/etc.)

Is there a known method to find a set of $\theta$ such that at least one eigenvalue of $A(\theta)$ is purely real?

Assume $A(\theta)$ is a real square matrix whose elements are linear functions of a real scalar $\theta$. I am interested in a general case (not assuming $A$ is symmetric/positive-definite/etc.)

Source Link
CWC
CWC
  • 433
  • 2
  • 10

Finding $\theta$ such that at least one eigenvalue of $A(\theta)$ is real

Is there a known method to find a set of $\theta$ such that at least one eigenvalue of $A(\theta)$ is purely real?

Assume $A(\theta)$ is a real square matrix whose elements are linear functions of a real scalar $\theta$. I am interested in a general case (not assume $A$ is symmetric/positive-definite/etc.)