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Generalized singular value decomposition

Index Generalized singular value decomposition

In linear algebra, the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition. [1]

14 relations: Charles F. Van Loan, Condition number, Correspondence analysis, Gene H. Golub, Identity matrix, LAPACK, Linear algebra, Linear discriminant analysis, Matrix decomposition, Multidimensional scaling, Norm (mathematics), Regularization (mathematics), Singular-value decomposition, Unitary matrix.

Charles F. Van Loan

Charles Francis Van Loan is an emeritus professor of computer science and the Joseph C. Ford Professor of Engineering at Cornell University,.

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Condition number

In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument.

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Correspondence analysis

Correspondence analysis (CA) or reciprocal averaging is a multivariate statistical technique proposed by Hirschfeld and later developed by Jean-Paul Benzécri.

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Gene H. Golub

Gene Howard Golub (February 29, 1932 – November 16, 2007), Fletcher Jones Professor of Computer Science (and, by courtesy, of Electrical Engineering) at Stanford University, was one of the preeminent numerical analysts of his generation.

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Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

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LAPACK

LAPACK (Linear Algebra Package) is a standard software library for numerical linear algebra.

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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Linear discriminant analysis

Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events.

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Matrix decomposition

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices.

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Multidimensional scaling

Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Regularization (mathematics)

In mathematics, statistics, and computer science, particularly in the fields of machine learning and inverse problems, regularization is a process of introducing additional information in order to solve an ill-posed problem or to prevent overfitting.

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Singular-value decomposition

In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix.

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Unitary matrix

In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.

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Generalized singular-value decomposition, Gsvd.

References

[1] https://en.wikipedia.org/wiki/Generalized_singular_value_decomposition

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