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which reduce to (17), (18) if A is the unit matrix and c = 0.
where A j is a square semi-definite matrix and c j is a real constant.
where I is the N×N identity matrix and c is the Welch bound given by (3).
where A is a given M × N real matrix, and C and Q are nonempty, closed and convex subsets in R N and R M, respectively.
Let A be a regular (ntimes n) matrix, B be an (ntimes q) matrix, and C be a regular (qtimes q) matrix.
Let A be a regular n × n matrix, B be an n × q matrix, and C be a q × q regular matrix.
Similar(36)
where f is the frequency in Hz, l is the loop-length in meters, H diag ( d ) = diag H ( d ) is a diagonal matrix of the DM channel H d), I is the N × N identity matrix, and C d)is a zero-diagonal matrix that reflects the crosstalk coupling dispersion (and extend the 99% crosstalk model) as per the existing standard, including the phase.
Precisely, we assume X t is a four-dimensional random vector of parameters whose realization is to be estimated and has mean E(X t) and covariance matrix C t, and X c is a four-dimensional random vector with zero mean and covariance matrix C c and is uncorrelated with X t, where E denotes the expectation operation.
(a any matrix, where and ; (b)any matrix, where and ; (c)any matrix, where and.
Proof: Let A and B are two stochastic matrices, and C = A.B is their product.
Where (a) and (b) correspond to the case of full covariance matrices and, (c) and (d) correspond to the case of diagonal covariance matrices.
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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