As matrices are used in physics to describe, for examples, rotations, the eigenvalues describe the values that do not change during this transformation (i.e. the axis of rotation) - I think that is one of the simplest examples.
Eigenvalues show you how strong the system is in it's corresponding eigenvector direction.
The physical significance of the eigenvalues and eigenvectors of a given matrix depends on fact that what physical quantity the matrix represents. for example when it represents the inertial properties of the solid body regarding the rotations the physical significance of eigenvectors is they are the main axes of inertria and the eigenvalues are the inertia moment regarding these axes.
In general, I can say that the eigenvectors of a matrix are those direction in the space that after the matrix operating on them, they supply the same direction with some coefficient of proportionality between "old" and "new" direction that are eigenvalues.
Yes, Bejo is right. The significance i gave you is based on detection of signals in a telecom system. For example, if you know the signal subspace, large eigenvalues would tell you that you are receiving signals in their corresponding eigenvector direction. Small eigenvalues would normally represent background noise or other fluctuations (disturbance) in the system.
Good luck
Eigenvalues the typical maximum root module matrix that is regular, square and positive. Calculation of the maximum module is connected eingavectors. There are two vectors: vector stability of the distribution (ie, right) and the left (vector of reproductive values). I do not know where you want to apply matrix calculus, but if they are biological systems, animal or plant populations can send you some papers about it, or look at a book Hall Caswel Matrix population models, 2001, 2007.
Dear Srujana,
It would be better to kindly state the domain you are working with (i.e. biology, dynamics, statistics, etc .. )
what is the physical significance of the eigen values and eigen vectors of
a) correlation coefficient matrix
b) heat kernel matrix
c)laplacian matrix
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