Glossary
- Matrix:
-
A rectangular tableau of numbers
- Eigenvalues:
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A set of numbers (real or complex) intrinsic to a given matrix
- Eigenvectors:
-
A set of vectors associated to a matrix transformation
- Singular Value Decomposition:
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A specific decomposition of any given matrix, useful in matrix analysis and its applications
Definition
Eigenvalues and Eigenvectors
Given a square (n × n) matrix A, a (complex) number λ is called an eigenvalue of A if there exists a nonzero n-dimensional column vector X such that
A vector X satisfying (1) is called an eigenvector of A corresponding to eigenvalue λ.
Singular Value Decomposition (SVD)
Given any rectangular matrix (m × n) matrix A, by singular value decomposition of the matrix A, we mean a decomposition of the form A = U Σ V T, where U and V are orthogonal matrices (representing rotations) and Σ is a diagonal matrix (representing a...
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Cascaval, R.C. (2018). Eigenvalues: Singular Value Decomposition. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7131-2_142
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