Transformation matrix - how to apply transform?

Hello, please help me to figure out how TM works. How to apply transformation only for matrix? Without applying transformation with bpy.ops.object.transformationApply. Please help.

I’ve wrote this Blender add-on. It allows you to change the transformation of objects using the text editor in Blender. Is this what you are looking for?

Here is a screenshot showing the menu entries:

If you are looking for Python code, setting the transformation matrix is quite simple:

import bpy
import numpy as np
matrix_world = np.identity(4, dtype=float)
bpy.context.object.matrix_world = matrix_world