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I am not sure this is the right section to ask this question, but here it goes. So, I was studying Stat. Physics and I came across this paper, A Mathematical Theory of Communication. What it's so important about this paper?
Importance of "A Mathematical Theory of Communication"
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"A Mathematical Theory of Communication" is crucial as it introduces the concept of entropy in both mathematics and physics, serving as a measure of disorder. This paper lays the groundwork for information theory, allowing for the characterization of uncertainties in complex systems. Shannon's definition of entropy is pivotal in managing multiple bit and particle systems. The discussion highlights its foundational role in connecting statistical mechanics and information theory. Understanding this paper is essential for grasping the interplay between these fields.
Obviously, there is something elementary I am missing here.
To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix
in the real plane; taking the transpose we get
which then corresponds to a-bi...
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