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indicate the transpose for real.
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A superscript is used to indicate the transpose of a matrix or vector, such as, and denotes the Hermitian transpose, for example,.
We use T to indicate the matrix transpose.
ε, H, T r, rank, indicate the expectation, Hermitian transpose, trace, and rank, respectively.
The superscript T means the transpose for matrices.
where H indicates the conjugate transpose (Hermitian) of a matrix (vector).
respectively, where N l is the number of Fourier modes contained in Z l and * indicates the conjugate transpose.
Let us call those columns I i for i = {1,2,…, 8}; we calculate the covariance matrix of the image C I [ 22]: (3) C I = E { (I − m I ) (I − m I ) T }, T indicates the matrix transpose.
Furthermore, and indicate the norm of scalar and vector while,, and stand for the transpose, conjugate, and conjugate transpose, respectively.
where indicates the complex conjugate transpose and denotes the determinant of.
Here −1 indicates to take the inverse of a matrix and T indicates to take the transpose of a matrix.
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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