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kgirish
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I want to know what exactly Eigen value imply. What is its Physical significance ? Physical significance of eigen vector? Does eigen value concept apply in signal processing or evalvating frequency response off a system?
Eigenvalues and eigenvectors are mathematical concepts that are widely used in the field of physics. In physics, eigenvalues represent the possible outcomes or values of a physical system, while eigenvectors represent the corresponding state or configuration of the system. They are important in understanding the behavior and properties of physical systems, such as atoms, molecules, and quantum particles.
In quantum mechanics, eigenvalues and eigenvectors play a crucial role in understanding the behavior and properties of quantum systems. They represent the possible energy levels and corresponding states of a quantum system, and are used to solve the Schrödinger equation, which describes the evolution of quantum systems over time.
No, eigenvalues and eigenvectors themselves cannot be physically observed. They are mathematical concepts that are used to describe physical systems and their properties. However, the physical effects and behaviors of a system can be observed and measured, which are related to the eigenvalues and eigenvectors of the system.
Eigenvalues and eigenvectors are related in that a specific eigenvalue corresponds to a specific eigenvector. In other words, an eigenvector is a vector that, when multiplied by a particular eigenvalue, produces the same vector, but scaled by that eigenvalue. This relationship is important in understanding the behavior and properties of physical systems.
In physics, the eigenvalues and eigenvectors of a system can provide information about the stability of the system. If the eigenvalues are all real and negative, the system is considered stable. If there are any positive or complex eigenvalues, the system is considered unstable. This is important in predicting the behavior and evolution of physical systems over time.