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Spectral Tuning in Biology I: Pigments,epresentation of the elements of the group by means of permutations; the properties of the latter may then be exploited to study the structure of the group. Instead of permutations, one may turn to linear transformations of a vector space, and consider homomorphisms of the group into a general lineaGONG 发表于 2025-3-22 12:05:33
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https://doi.org/10.1007/978-981-10-5493-8efore .. = ... = .. = . = .; hence .. is neutral on the right for all . ∈ ., and similarly there exists .., neutral on the left. Multiplication of the two gives .... = .., .... = .., and .) follows. As for .), solving . = . and . = ., if . = . we have . = . from which . = ., i.e. . = . and . = .; he饮料 发表于 2025-3-22 17:14:05
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Representations,group. Instead of permutations, one may turn to linear transformations of a vector space, and consider homomorphisms of the group into a general linear group; in this way many group-theoretic problems may be reduced to problems in linear algebra.短程旅游 发表于 2025-3-23 08:28:34
Solution to the exercises, two gives .... = .., .... = .., and .) follows. As for .), solving . = . and . = ., if . = . we have . = . from which . = ., i.e. . = . and . = .; hence the right inverse is unique, and so is the left inverse. If . = ., then . = . = . = . = . = . = . and . = . = ..