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Exact(31)
It presents the mathematical relationship between two matrices of any size.
Then there exist two matrices of order and of order such that (2.20).
Thus, a new group ('OHgly') was introduced and two matrices of parameters were adjusted.
Thus, A is the sum of two matrices of rank 1 and, hence, at most of rank 2.
In mathematics, the kronecker product is an operation on two matrices of arbitrary size resulting in a block matrix [14].
By using Equation 13, the two matrices of A and B are constructed from the estimated sensitivity parameters, and the spectral and the spatial matrices as and.
Similar(29)
Here I and O are the identity and zero matrices of size (3times 3), respectively.
The mutation operator is done in all four matrices of solution chromosome.
By I and 0 we denote the identity and zero matrices of appropriate dimensions, respectively.
Clearly, the zeros of this matrix are zero matrices of size ( M + 1 ) ( N + 1 ) × ( M + 1 ) ( N + 1 ).
Further, if B and D are zero matrices of order n, then (DM1) becomes the dual model considered in [14].
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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