frobenius.prod: 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
Value
A numeric value.
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 \(\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {x_{i,j} \;y_{i,j} } } \).
References
Styan, G. P. H. (1973). Hadamard Products and Multivariate Statistical Analysis,
Linear Algebra and Its Applications, Elsevier, 6, 217-240.