inner product for datasets with vector scale
An rmult object is considered as a sequence of vectors. The %*%
is considered as the inner multiplication. An inner multiplication with
another vector is the scalar product. an inner multiplication with
a matrix is a matrix multiplication, where the rmult-vectors are either
considered as row or as column vector.
## S3 method for class 'rmult' x %*% y
x |
an rmult vector or dataset of vectors, a numeric vector of
length ( |
y |
an rmult vector or dataset of vectors , a numeric vector of
length ( |
The operators try to minic the behavior of %*% on
c()-vectors as inner product applied in parallel to all vectors of
the dataset. Thus the product of a vector with another rmult
object or unclassed vector v results in the scalar product. For
the multiplication with a matrix each vector is considered as a row or
column, whatever is more appropriate.
an object of class "rmult" or a numeric vector containing the
result of the
corresponding inner products.
The product x %*% A %*% y is associative.
K.Gerald v.d. Boogaart http://www.stat.boogaart.de
x <- rmult(matrix( sqrt(1:12), ncol= 3 )) x%*%x A <- matrix( 1:9,nrow=3) x %*% A %*% x x %*% A A %*% x x %*% 1:3 x %*% 1:3 1:3 %*% x
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