Matrix calculus

  1. Find the derivatives of
  2. Find , if .
  3. Find , if .
  4. Find , if .
  5. Find the gradient and hessian , if .
  6. Find , if .
  7. Find , if .
  8. Find , if .
  9. Find , if

    Note: here under assumes first order approximation of using Taylor series:

  10. Find , if

    Note: here under assumes second order approximation of using Taylor series:

  11. Find gradient and hessian of , if:

  12. What is the gradient, Jacobian, Hessian? Is there any connection between those three definitions?
  13. Calculate:
  14. Calculate the Frobenious norm derivative:
  15. Calculate the gradient of the softmax regression in binary case () - dimensional objects:

  16. Find , if
  17. Find , if
  18. Find , if
  19. Find the gradient and hessian , if

  20. Find the gradient and hessian , if
  21. Calculate , if
  22. Calculate the derivatives of the loss function with respect to parameters for the single object (or, )
  23. Find the gradient and hessian , if
  24. Find the gradient and hessian , if
  25. Find the gradient and hessian , if
  26. Find the gradient and hessian , if