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Assuming, each entity of matrix and in (21) and (22) reduce to.
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For the conjugate situation, assuming, in the same way we can get each entity of matrices and in (25) and (26): (55).
We use (alpha ^{n}_{ijm}) to denote the entity at position (m,m) of ({mathbf {U}^{n}_{ij}}^{H}mathbf {H}^{n}_{ij}mathbf {Q}^{n}_{j}mathbf {V}^{n}_{ij}) and use (p^{n}_{ijm}) to denote the entity at position (m,m) of matrix (mathbf {P}^{n}_{ij}).
Matthew Hodgson of Matrix tells a similar story.
First, the two components of an RVC form a compound, a word-level entity, but the matrix verb of a V-DE construction like 56 and the predicate of the clause marked by -de are not in the same clause and obviously do not form a compound.
"UNAMA is an entity of whom?
"It is an entity of its own".
The disease entity of depression was questioned.
Synthesis of metal nanoparticles either in the form of independent entities or in matrices thus assume significance and are of interest to chemists and physicists alike.
He formalized the theory of matrices.
Matrix groups consist of matrices together with matrix multiplication.
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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