Cryptocurrency Q&A
Is The Matrix abelian?
Is The Matrix abelian?
Margherita
Wed Aug 14 2024
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6 answers
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Excuse me, but I'm curious to know if you've given any thought to the question, "Is The Matrix abelian?" It's an intriguing concept to ponder, especially when considering the mathematical underpinnings of the film's universe. An abelian group, as you know, is one in which the order of operations doesn't affect the result. So, when we think about the way the Matrix operates, could it be said to exhibit abelian properties? I'm genuinely interested in your thoughts on this matter.
6 answers
SakuraSpiritual
Fri Aug 16 2024
The realm of mathematics, particularly in the context of matrices, presents intricate structures that are fundamental to our understanding of various algebraic systems.
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CryptoPioneer
Fri Aug 16 2024
The set Mn(R), comprising all n × n real matrices, under the operation of addition, forms an abelian group. This means that the set satisfies all the group axioms, including closure, associativity, identity, and invertibility, with the added property of commutativity.
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Martina
Fri Aug 16 2024
However, when we consider the same set Mn(R) but with the operation of matrix multiplication, the picture changes drastically. Matrix multiplication does not necessarily yield a group structure.
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WhisperVoyager
Thu Aug 15 2024
One significant obstacle to forming a group under matrix multiplication is the existence of inverses. Notably, the zero matrix, which is a member of Mn(R), does not possess an inverse under matrix multiplication.
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KimchiQueenCharm
Thu Aug 15 2024
The absence of inverses for certain elements, particularly the zero matrix, violates one of the fundamental group axioms, thereby disqualifying Mn(R) with matrix multiplication as a group.
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