653:. I disagree with the respondent on Quora, who said "To understand what "kernel" means in math, you need some background. It makes no sense to try and learn these things from Knowledge. This is like trying to learn a language using only a dictionary." Nonsense: it makes sense to try to learn what the concept is on Knowledge, and Knowledge has far more utility than a dictionary. Ironically, he then proceeds to explain it fairly well like someone might do on Knowledge, and better than this page currently does for me. Crucially, more accessible explanations will not use such technical terms as "homomorphism" or "injective". I comment here in hopes that more knuckleheads can appreciate mathematical concepts that are actually pretty accessible.
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I think this was intended to refer to Mal'cev algebras in the sense of general algebra, which are indeed structures for which knowing the kernel in the simpler sense suffices to construct the whole kernel: specifically, all reflexive relations closed under the operations are automatically equivalence
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Knucklehead here. I was reading about kernel methods and I wondered what a kernel was mathematically. So I came here, and the intro is incomprehensible to me. I'm wondering if those fond of this page might consider using plainer, less technical language to describe what it is initially. Examples of
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Could someone explain how this is or is not the same as the kernel of a convolution? It seems to be different in that a convolution is linear yet in general only the zero vector maps to zero (I think).
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Aren't Mal'cev algebras supposed to be non-associative algebras, which in turn are supposed to be modules? If a module needs to be an abelian group, how can a non-abelian group be a Mal'cev algebra?
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You are wrong, the article correctly asserts that the kernel is a non-unital ring but is not a unital ring, unless if the target of the homomorphism is the zero ring.
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I have rewritten the lead for making it less technical (and also less vague). In particular, I have added a definition for the unavoidable technical terms.
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can the editor of this article give me suggestions on how to make this picture consistent with the terminology of this article, thanks--
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This section incorrectly states "It turns out that, although ker f is generally not a subring of R," but this is false (
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describes something that groups definitely are not, so what is a Mal'cev algebra in the context of this article here?
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Knowledge. If you would like to participate, please visit the project page, where you can join
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Apparently, Mal'cev algebra refers to a generalization of groups that has neutral element
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Surely additive groups are Mal'cev algebras when equipped withe the zero product. But
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relations. But I don't know what the original editor meant about a neutral element.
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I have changed "group" into "commutative group". I hope that ths solves the problem.
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Null space and kernel are taught as different concepts in different contexts. --
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The article speaks of groups as being Mal'cev algebras, but the linked article
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Considering they are directly related, no reason not to have them merged.
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