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dexterdev
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What is eigen value, eigen vector etc and what is their physical significance?
-Devanand T
-Devanand T
Simon Bridge said:These need have no physical significance at all - the terminology is mathematical and describes a mathematical relationship.
An eigenvalue is a scalar value that represents the amount by which an eigenvector is scaled when it is multiplied by a given matrix. An eigenvector is a non-zero vector that, when multiplied by a matrix, remains in the same direction but may be scaled by a certain factor.
Eigenvalues and eigenvectors are important because they allow us to understand the behavior of linear transformations on a vector space. They can also be used to find the directions in which a matrix stretches or compresses a given set of vectors.
Eigenvalues and eigenvectors are used in a variety of scientific fields, such as physics, engineering, and statistics. They are commonly used in data analysis, image processing, and in solving differential equations.
In physics, eigenvalues and eigenvectors can represent important physical quantities, such as the energy levels of a quantum mechanical system or the principal axes of a rigid body. In engineering, they can be used to analyze the stability and behavior of structures under different conditions.
Yes, eigenvalues and eigenvectors can have complex values. This is often the case when dealing with matrices that have complex entries. In this case, the eigenvectors may also have complex entries, but their magnitude and direction remain the same.