| frobenius.prod {matrixcalc} | R Documentation |
Frobenius innter product of matrices
Description
This function returns the Fronbenius inner product of two matrices, x and y, with the same row and column dimensions.
Usage
frobenius.prod(x, y)
Arguments
x |
a numeric matrix or vector object |
y |
a numeric matrix or vector object |
Details
The Frobenius inner product is the element-by-element sum of
the Hadamard or Shur product of two numeric matrices. Let {\bf{x}} and
{\bf{y}} be two m \times n matrices. Then Frobenious inner product
is computed as \sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {x_{i,j} \;y_{i,j} } } .
Value
A numeric value.
Note
The function converts vectors to matrices if necessary. The function stops running if x or y is not numeric and an error message is displayed. The function also stops running if x and y do not have the same row and column dimensions and an error mesage is displayed.
Author(s)
Frederick Novomestky fnovomes@poly.edu
References
Styan, G. P. H. (1973). Hadamard Products and Multivariate Statistical Analysis, Linear Algebra and Its Applications, Elsevier, 6, 217-240.
See Also
Examples
x <- matrix( c( 1, 2, 3, 4 ), nrow=2, byrow=TRUE )
y <- matrix( c( 2, 4, 6, 8 ), nrow=2, byrow=TRUE )
z <- frobenius.prod( x, y )
print( z )