acompscalarproduct {compositions} | R Documentation |

## inner product for datasets with a vector space structure

### Description

acomp and aplus objects are considered as (sets 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
vectors are either considered as row or as column vector.

### Usage

```
## S3 method for class 'acomp'
x %*% y
## S3 method for class 'aplus'
x %*% y
```

### Arguments

`x` |
a acomp or aplus object or a matrix interpreted in clr, ilr or ilt coordinates |

`y` |
a acomp or aplus object or a matrix interpreted in clr, ilr or ilt coordinates |

### Details

The operators try to mimic the behavior of `%*%`

on
`c()`

-vectors as inner product, applied in parallel to all row-vectors of
the dataset. Thus the product of a vector with a vector of the same
type results in the scalar product of both. For the multiplication with a matrix
each vector is considered as a row or column, whatever is more
appropriate. The matrix itself is considered as representing a linear
mapping (endomorphism) of the vector space to a space of the same type. The mapping is
represented in clr, ilr or ilt coordinates. Which of the aforementioned
coordinate systems is used is judged from the type of `x` and from
the dimensions of the `A`.

### Value

Either a numeric vector containing the scalar products, or an object of type acomp or aplus containing the vectors transformed with the given matrix.

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### See Also

### Examples

```
x <- acomp(matrix( sqrt(1:12), ncol= 3 ))
x%*%x
A <- matrix( 1:9,nrow=3)
x %*% A %*% x
x %*% A
A %*% x
A <- matrix( 1:4,nrow=2)
x %*% A %*% x
x %*% A
A %*% x
x <- aplus(matrix( sqrt(1:12), ncol= 3 ))
x%*%x
A <- matrix( 1:9,nrow=3)
x %*% A %*% x
x %*% A
A %*% x
```

*compositions*version 2.0-8 Index]