# GSVD_English: Generalized Singular Value Decomposition (GSVD). In MFAg: Multiple Factor Analysis (MFA)

## Description

Given the matrix A of order nxm, the generalized singular value decomposition (GSVD) involves the use of two sets of positive square matrices of order nxn and mxm respectively. These two matrices express constraints imposed, respectively, on the lines and columns of A.

## Usage

 `1` ```GSVD(data, plin = NULL, pcol = NULL) ```

## Arguments

 `data` Matrix used for decomposition. `plin` Weight for rows. `pcol` Weight for columns

## Details

If plin or pcol is not used, it will be calculated as the usual singular value decomposition.

## Value

 `d` Eigenvalues, that is, line vector with singular values of the decomposition. `u` Eigenvectors referring rows. `v` Eigenvectors referring columns.

## Author(s)

Paulo Cesar Ossani

Marcelo Angelo Cirillo

## References

ABDI, H. Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In: SALKIND, N. J. (Ed.). Encyclopedia of measurement and statistics. Thousand Oaks: Sage, 2007. p. 907-912.

## Examples

 ```1 2 3 4 5 6 7 8``` ```data <- matrix(c(1,2,3,4,5,6,7,8,9,10,11,12), nrow = 4, ncol = 3) svd(data) # Usual Singular Value Decomposition GSVD(data) # GSVD with the same previous results # GSVD with weights for rows and columns GSVD(data, plin = c(0.1,0.5,2,1.5), pcol = c(1.3,2,0.8)) ```

MFAg documentation built on Jan. 13, 2021, 6:39 p.m.