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Kubilay Yazoglu
- 8
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Hey there, I'm thinking about if one of the eigenvalues is zero (means determinant is 0. right?) So, is there any possibility to non-zero eigenvalue also exists?
Yesmathwonk said:another point of view is that eigenvalues are roots of the characteristic polynomial. so if one root is zero can other roots be non zero?
Eigenvalues are a concept in linear algebra that represent the scale factor by which a vector is stretched or compressed when multiplied by a matrix. They are also known as characteristic values or latent roots.
Eigenvalues are useful in many areas of mathematics and science, including quantum mechanics, signal processing, and data analysis. They provide important information about the behavior and properties of a linear transformation.
The calculation of eigenvalues involves finding the roots of the characteristic polynomial of a matrix, which is obtained by subtracting a scalar variable from the main diagonal of the matrix and taking its determinant. This results in an algebraic equation, the solutions of which are the eigenvalues.
Eigenvectors are the corresponding vectors to eigenvalues and represent the direction of the stretching or compression. They are also known as characteristic vectors. The eigenvalue and eigenvector of a matrix are related by the equation Ax = λx, where A is the matrix, λ is the eigenvalue, and x is the eigenvector.
Eigenvalues are used in data analysis to reduce the dimensionality of a dataset and identify the most important features or patterns. This is done by calculating the eigenvalues and eigenvectors of the covariance matrix of the data and selecting the top eigenvectors based on their corresponding eigenvalues.