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svishal03
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Please can anyone provide an insight into what do complex eigen values physically indicate?
Vishal
Vishal
The eigenvalues are imaginary in case of vibration without damping
A purely real eigenvalue means that the solutions are exponential and decay directly to zero (since it is impossible to have a positive eigenvalue)
svishal03 said:@Boneh3d:
You said:
Did you mean a pure real eigen value would indicate that the system is stationary?
move exponentially to the equilibrium position
Complex eigenvalues are a mathematical concept used in linear algebra to describe the behavior of certain systems, such as matrices, vectors, and differential equations. They represent the values that satisfy the characteristic equation of a system, which is used to describe its behavior.
Real eigenvalues are numbers that have a physical meaning in a system, such as the rate of change or the frequency of oscillation. Complex eigenvalues, on the other hand, do not have a direct physical interpretation but are used in combination with real eigenvalues to describe the overall behavior of a system.
Complex eigenvalues provide insight into the behavior of systems that exhibit oscillatory or rotating behavior. They can also help in understanding the stability and convergence of a system, as well as the relationship between different variables in a system.
Complex eigenvalues are used in various fields of science, including physics, engineering, and mathematics. They are used to analyze and model systems, such as electrical circuits, mechanical systems, and quantum systems. They also play a crucial role in solving differential equations, which are used to describe many physical phenomena.
Yes, complex eigenvalues have many real-world applications, especially in fields such as signal processing, control systems, and quantum mechanics. They are used in designing and analyzing systems, predicting the behavior of physical systems, and developing new technologies.