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They have flocked to these films, and to others like The Matrix and Being John Malkovich, which dare grapple with 21st century questions of virtual reality and altered consciousness.
where is the null matrix and is the identity matrix.
where is an observable random matrix,,, and are known matrices, respectively., are unknown matrices.
where is the matrix of priors, is the state transition matrix, and is the observation matrix.
where " " is the unit matrix and " " is the transpose operator.
Let be a Walsh-Hadamard matrix and be expressed as.
The matrix is the identity matrix, and is the vector of NodeB transmit powers.
Since is a circulant matrix and is a circulant matrix, the product of and is also a circulant matrix.
Let us split into two matrices and such that, where is an matrix and is an matrix.
The superscript denotes the transpose, is a diagonal matrix, and is an identity matrix of size.
where is a 1-by-1 identity matrix, is a 1-by zero matrix, is a nonzero -by-1 matris, and is a -by- 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