GLM - Matrix from orientation is creating row major and not column major matrix?

Question

After figuring out the answer to my previous question I have found the cause to be some kind of mathematical oddity.

Using the GLM (OpenGL) library I create an orientation as follows

glm::gtx::quaternion::orientation = 
    glm::gtx::quaternion::angleAxis(pitchAccum, 1.0f, 0.0f, 0.0f) * 
    glm::gtx::quaternion::angleAxis(yawAccum, 0.0f, 1.0f, 0.0f);

Now if I create a matrix from this orientation it is no longer column major but somehow becomes row major

    glm::mat4 view = glm::gtx::quaternion::toMat4(orientation); 

In other words the 3 coordinates axes are found by accessing the matrix using row major indices

view[0][0], view[1][0], view[2][0]  // X axis
view[0][1], view[1][1], view[2][1]  // Y axis
view[0][2], view[1][2], view[2][2]  // Z axis

In other words the transpose of the rotation part.

The translation part of the matrix should still be set using column major in order for the final view matrix to work as intended.

view[3][0] = -glm::dot(glm::vec3(view[0][0], view[1][0], view[2][0]), position);    // Right
view[3][1] = -glm::dot(glm::vec3(view[0][1], view[1][1], view[2][1]), position);    // Up
view[3][2] = -glm::dot(glm::vec3(view[0][2], view[1][2], view[2][2]), position);    // Forward

Why is the rotation matrix flipped from column major to row major (transposed?) when using the orientation?

EDIT:

// Move forward
if (glfwGetKey('W') == GLFW_PRESS)
{
    //movement += glm::vec3(view[2][0], view[2][1], view[2][2]);  // incorrect
    movement += -glm::vec3(view[0][2], view[1][2], view[2][2]);   // correct
}
// Move backward
if (glfwGetKey('S') == GLFW_PRESS)
{
    //movement += -glm::vec3(view[2][0], view[2][1], view[2][2]); // incorrect
    movement += glm::vec3(view[0][2], view[1][2], view[2][2]);    // correct
}
// Strafe left
if (glfwGetKey('A') == GLFW_PRESS)
{
    //movement += -glm::vec3(view[0][0], view[0][1], view[0][2]);  // incorrect
    movement += -glm::vec3(view[0][0], view[1][0], view[2][0]);    // correct
}
// Strafe right
if (glfwGetKey('D') == GLFW_PRESS)
{
    //movement += glm::vec3(view[0][0], view[0][1], view[0][2]);  // incorrect
    movement += glm::vec3(view[0][0], view[1][0], view[2][0]);    // correct
}

Answer 1

A matrix M which transforms from the space A to the space B has the basis vectors of space A, but expressed relative to space B.

The camera matrix transforms from world space to camera space. Thus, the basis vectors of the camera matrix are the basis vectors of world space , as seen from camera space. Not the basis vectors of camera space .

The orientation of the camera, relative to world space, is the inverse of this transformation. And since the inverse of a rotation matrix is it's transpose , you have your issue.

The problem isn't with the matrix; the problem is with the difference between what you think the matrix says and what it actually says.