Logic Masters Deutschland e.V.

This is my very first sudoku puzzle ever created, inspired by the CTC monthly puzzle theme of CLASSROOM

The rules are as follows:
1. Normal sudoku rules apply
2. Every arrow would diagonally determine a square matrix. The number in the circles (reading from left to right, from top to bottom) is the determinant of the corresponding matrix
3. For all the 3x3 matrices, the middle entries must be the smallest within the bottom-right 2x2 matrix
4. Digits on the open side of a greater than sign is greater than the other side

CTC Link
F-puzzles Link

Enjoy!