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eigenvector matrix

An eigenvector matrix is a matrix whose columns or rows are formed by the eigenvectors of a given square matrix, typically ordered to align with their corresponding eigenvalues. In linear algebra, it functions as a transformation matrix that facilitates spectral decomposition and diagonalization, converting a matrix into a diagonal matrix of its eigenvalues. When derived from a real symmetric matrix, such as a similarity, affinity, or graph Laplacian matrix, the eigenvector matrix can be constructed as an orthogonal matrix containing mutually perpendicular unit-length vectors. In data analysis, dimensionality reduction, and spectral clustering, an eigenvector matrix composed of selected leading or trailing eigenvectors projects high-dimensional data into a lower-dimensional geometric space, revealing latent structures, principal directions of variation, and separable cluster groupings.

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