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I have been taking a lot of courses concerning data science, and one algebraic concept that I have learned about is the study of eigenvalues and eigenvectors. In linear algebra, an eigenvector, or characteristic vector of a linear transformation is a non-zero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, denoted by the symbol 𝛌, is the factor by which the eigenvector is scaled.
Eigenvalues and eigenvectors feature prominently in the analysis of linear transformations. Eigenvalues and eigenvectors have a wide range of applications, for example in stability analysis, vibration analysis, atomic orbitals, facial recognition, and matrix diagonalisation.
For a square matrix, A, an eigenvector and eigenvalue make this equation true:-
Where A is the matrix, v is the eigenvector, and 𝛌 is the eigenvalue.
A good introductory tutorial, which I have studied to create this blog post, can be found here:- https://www.mathsisfun.com/algebra/eigenvalue.html
The Python programming language has the capacity to compute eigenvalues and eigenvectors through the numpy library.
The numpy.linalg.eig function computes the eigenvalues and the right eigenvectors of a…
