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- W97833419 abstract "In the preceding chapters we analyzed some properties of a vector space E(_{textit{n}}). In this chapter we introduce into E(_{textit{n}}) two other operations: the scalar product and the antiscalar product. A vector space equipped with the first operation is called a Euclidean vector space, whereas when it is equipped with the second operation, it is said to be a symplectic vector space. These operations allow us to introduce into E(_{textit{n}}) many other geometric and algebraic concepts such as length of a vector, orthogonality between two vectors, etc. Further, eigenvalues and eigenvectors of a linear map are analyzed together with orthogonal transformations of (E_n). Finally, symplectic vector spaces are introduced and some their properties studied." @default.
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- W97833419 date "2012-01-01" @default.
- W97833419 modified "2023-09-23" @default.
- W97833419 title "Euclidean and Symplectic Vector Spaces" @default.
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- W97833419 doi "https://doi.org/10.1007/978-0-8176-8352-8_4" @default.
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