Eigenvalues
Eigenvalues are a fundamental concept in linear algebra and are used extensively in data science and machine learning. In simple terms, eigenvalues are the values that represent how a linear transformation changes a vector. They are the solutions to the equation Av = λv, where A is a square matrix, λ is the eigenvalue, and v is the eigenvector. Eigenvalues are important in data science because they can be used to reduce the dimensionality of a dataset, which can make it easier to analyze and visualize. They are also used in principal component analysis (PCA), a technique used to identify patterns in high-dimensional data. In machine learning, eigenvalues are used in algorithms such as singular value decomposition (SVD) and eigenvalue decomposition (EVD), which are used to extract features from data and reduce noise.
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