# isPureRotationMatrix: Determine if the variable is a pure rotation matrix In RSpincalc: Conversion Between Attitude Representations of DCM, Euler Angles, Quaternions, and Euler Vectors

## Description

`isPureRotationMatrix` determines if a matrix is pure rotation matrix (proper orthogonal matrix) with det(m)==1. `isPureQuaternion` determines if a quaternion is a pure quaternion. `isRealQuaternion` determines if a quaternion is a real quaternion. `isUnitQuaternion` determines if a quaternion is a unit quaternion.

## Usage

 `1` ```isPureRotationMatrix(DCM, tol = 0.01) ```

## Arguments

 `DCM` Direction Cosine Matrix (DCM) is a rotation matrix 3x3 (N=1) or an array 3x3xN. `tol` Tolerance value.

## Value

Logical, TRUE = matrix is pure rotation matrix.

## Author(s)

Jose Gama

`Q2GL`
 ```1 2 3 4 5``` ```isPureRotationMatrix(matrix(rep(0,9),3,3,byrow=TRUE),.1) isPureRotationMatrix(matrix(rep(1,9),3,3,byrow=TRUE),.1) isPureRotationMatrix(matrix(c(0,0,-1,0,1,0,1,0,1),3,3,byrow=TRUE),.1) DCMx10 <- DCMrandom(10) isPureRotationMatrix(DCMx10) ```