Transport of Structure
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, transport of structure is the definition of a new structure on an object by reference to another object on which a similar structure already exists. Definitions by transport of structure are regarded as canonical. Since mathematically structures are often defined in reference to an underlying spaces, many examples of transport of structure involve spaces and mappings between them. For example, if V and W are vector spaces, and if phi colon V to W is an…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, transport of structure is the definition of a new structure on an object by reference to another object on which a similar structure already exists. Definitions by transport of structure are regarded as canonical. Since mathematically structures are often defined in reference to an underlying spaces, many examples of transport of structure involve spaces and mappings between them. For example, if V and W are vector spaces, and if phi colon V to W is an isomorphism, and if (cdot,cdot) is an inner product on W, then we can define an inner product [cdot, cdot] on V by [v_1, v_2] = (phi(v_1), phi(v_2));.