title: Convert quaternion from right-handed to left-handed coordinate system
body: <p>I my 3d program, the rotation of object is represented by the quaternion like <code>[0.130526, 0.0, 0.0, 0.991445]</code>. The program works with right-handed coordinate system with the Z axis pointing up (like in 3ds max):</p>
  
  <p><img src="https://i.stack.imgur.com/JZsXJ.jpg" alt="enter image description here"></p>
  
  <p>On the other hand, my application use <strong>left-handed</strong> coordinate system <strong>and the Y axis is up</strong>:</p>
  
  <p><img src="https://i.stack.imgur.com/Xd4eh.png" alt="enter image description here"></p>
  
  <p>How can I transform my quaternion from one coordinate system to another, with the respect for which axis  is up?</p>