Difference between Direction cosine matrix (DCM) and rotation matrix

Question

I am a bit confused about the difference between direction cosine matrix(DCM) and rotation matrix. I have searched through the literature but found no explicit explanation if they are different or same and when should each of them be used. For DCM I have referred to this documents ([DCM][1]) and what I understood is that the DCM and rotation matrix for a Yaw,Pitch,Roll sequence can be calculated as shown in the code snippet below:

import math
import numpy as np

yaw     = np.deg2rad(90);
pitch   = np.deg2rad(0);
roll    = np.deg2rad(0);

yawMatrix = np.matrix([[math.cos(yaw), -math.sin(yaw), 0],
                        [math.sin(yaw), math.cos(yaw), 0],
                        [0, 0, 1]
                        ])
            
pitchMatrix = np.matrix([[math.cos(pitch), 0, math.sin(pitch)],
                        [0, 1, 0],
                        [-math.sin(pitch), 0, math.cos(pitch)]
                        ])
rollMatrix = np.matrix([[1, 0, 0],
                        [0, math.cos(roll), -math.sin(roll)],
                        [0, math.sin(roll), math.cos(roll)]
                        ])

R =  yawMatrix * pitchMatrix * rollMatrix

dcm_yaw = np.matrix([[math.cos(yaw), math.sin(yaw), 0],
                    [-math.sin(yaw), math.cos(yaw), 0],
                    [0, 0, 1]
                    ])
dcm_pitch = np.matrix([[math.cos(pitch), 0, -math.sin(pitch)],
                    [0, 1, 0],
                    [math.sin(pitch), 0, math.cos(pitch)]
                    ])
dcm_roll = np.matrix([[1, 0, 0],
                    [0, math.cos(roll), math.sin(roll)],
                    [0, -math.sin(roll), math.cos(roll)]
                    ])

DCM = dcm_yaw * dcm_pitch * dcm_roll

print(R)
print(DCM) 

Is this intepretation of DCM and rotation matrices correct? [1]: https://www.scribd.com/document/439833165/Directional-Cosine-Matrices

Answer 1

Yes DCM is a rotation matrix.

You can check it is defined as rotation matrix in this paper of the "MEMS inertial navigation systems for aircraft" https://www.sciencedirect.com/topics/engineering/direction-cosine-matrix

And in several other papers is regarded as member of SO(3) group, which means it is a rotation. Also, you can check the matrix is orthogonal and its determinant is equal to one, which is the dedinition of a rotation matrix.