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where is an real matrix.
where is an real matrix such that.
Now, let and and, and is an real matrix.
where is an real matrix such that and.
Although optimum scaling factor is an real value [10], the multiplication of real value is sublated in implementation due to the high complexity.
Suppose that is an positive definite matrix and is an real vector, then the well-known Kantorovich inequality can be expressed as (1.1).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com