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Multilinear algebra In mathematics multilinear algebra extends the methods of linear algebra . Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concept of a tensor and develops the theory of 'tensor spaces'. In applications, numerous types of tensors arise. The theory tries to be comprehensive, with a corresponding range of spaces and an account of their relationships. Historical background of the approach to multilinear algebra The subject itself has various roots going back to the mathematics of the nineteenth century, in what was then called tensor analysis , or the "tensor calculus of tensor fields". It developed out of the use of tensors in differential geometry general relativity , and many branches of applied mathematics . Around the middle of the 20th century the study of tensors was reformulated more abstractly. The Bourbaki group's treatise Multilinear Algebra was especially influential in fact the term multilinear algebra was probably coined there.

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Portals A-Z Categories Random ... discussion Page more Multilinear algebra In mathematics multilinear algebra extends the methods of linear algebra . Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces , multilinear algebra builds on the concept of a tensor and develops the theory of 'tensor spaces'. In applications, numerous types of tensors arise. The theory tries to be comprehensive, with a corresponding range of spaces and an account of their relationships. Contents Historical background of the approach to multilinear algebra Conclusion on the abstract approach Content of multilinear algebra From the point of view of applications ... edit Historical background of the approach to multilinear algebra The subject itself has various roots going back to the mathematics of the nineteenth century, in what was then called tensor analysis , or the " tensor calculus of tensor fields ". It developed out of the use of tensors in differential geometry general relativity , and many branches of applied mathematics . Around the middle of the 20th century the study of tensors was reformulated more abstractly. The Bourbaki group's treatise Multilinear Algebra multilinear algebra was probably coined there.

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