Eli5: what are eigen values and eigen vectors and how is it useful.
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Eigenvalues and eigenvectors are mathematical concepts that are used to study linear transformations. A linear transformation is a function that maps one vector to another vector in a way that preserves certain properties.
An eigenvector is a special vector that, when transformed by a linear transformation, only changes in magnitude (i.e., it gets stretched or shrunk) but not in direction. An eigenvalue is the scalar value that represents how much the eigenvector gets stretched or shrunk by the linear transformation.
Eigenvalues and eigenvectors are useful because they help us understand how a linear transformation affects vectors in space. They can be used to find important features of a matrix, such as its determinant and trace, which are important in many areas of mathematics and science.
For example, in physics, eigenvalues and eigenvectors are used to study the behavior of quantum mechanical systems. In engineering, they are used to analyze the stability of structures under different loads. In computer science, they are used in machine learning algorithms to reduce the dimensionality of data and extract important features.
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