rotationBetweenVectors

bool isAlmostZero4(Vector4f v)
{
    float e = 0.002f;

    return abs(v.x) < e &&
           abs(v.y) < e &&
           abs(v.z) < e &&
           abs(v.w) < e;
}

// build ModelView (World to Camera)
vec3 center = vec3(0.0f, 0.0f, 0.0f);
vec3 eye = center + vec3(0.0f, 1.0f, 1.0f);
vec3 up = vec3(0.0f, -0.707f, 0.707f);

Matrix4f modelView = lookAtMatrix(eye, center, up);

// build Projection (Camera to Eye)
Matrix4f projection = perspectiveMatrix(45.0f, 16.0f / 9.0f, 1.0f, 100.0f);

// compose into one transformation
Matrix4f projectionModelView = projection * modelView;

vec4 positionInWorld = vec4(0.0f, 0.0f, 0.0f, 1.0f);

vec4 transformed1 =
    positionInWorld * projectionModelView;

vec4 transformed2 =
    (positionInWorld * modelView) * projection;

assert(isAlmostZero4(transformed1 - transformed2));