Better in what way?
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Readability. You can look at a sequence of matrix operations and understand what it does, computationally, but outside common and familiar algorithms, the why and what part gets lost easily. What's this matrix represent? Where does the shape come from?
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When linear ops are used well, they reveal important structural features of your code or problem in ways that loops cannot. I think the apparent obfuscation comes not from linear algebra themselves but from the (nearly complete) lack of math training among most people that code.
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Often yes. But, I'm not talking about situations where the expression compresses information usefully because of familiarity -- e.g. a recognizable pseudo inverse or a decomposition.
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