# symm.prod: Matrix multiplication envolving the symmetrizer matrix In fastmatrix: Fast Computation of some Matrices Useful in Statistics

## Description

Given the order of a symmetrizer and matrix `x`, performs one of the matrix-matrix operations:

• \bold{Y} = \bold{NX}, if `side = "left"`, or

• \bold{Y} = \bold{XN}, if `side = "right"`,

where \bold{N} is the symmetrizer matrix of order n. The main aim of `symm.prod` is to do this matrix multiplication without forming the symmetrizer matrix.

## Usage

 `1` ```symm.prod(n = 1, x = NULL, side = "left") ```

## Arguments

 `n` order of the symmetrizer matrix. `x` numeric matrix (or vector). `side` a string selecting if symmetrizer matrix is pre-multiplying `x`, that is `side = "left"` or post-multiplying `x`, by using `side = "right"`.

## Details

Underlying `C` code only uses information provided by `symm.info` to performs the matrix multiplication. The symmetrizer matrix is never created.

`symmetrizer`
 ```1 2 3 4 5 6``` ```N4 <- symmetrizer(n = 4, matrix = TRUE) x <- matrix(1:32, ncol = 2) y <- N4 %*% x z <- symm.prod(n = 4, x) # N4 is not stored all(z == y) # matrices y and z are equal! ```