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2021
This chapter develops basic properties of complex Euclidean space. Some of the main ideas are unitary transformations, the holomorphic automorphism group of the unit ball, the use of Hermitian forms, and proper holomorphic mappings. We also gather some elementary combinatorial information.
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This chapter develops basic properties of complex Euclidean space. Some of the main ideas are unitary transformations, the holomorphic automorphism group of the unit ball, the use of Hermitian forms, and proper holomorphic mappings. We also gather some elementary combinatorial information.
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2013
The study of the Euclidean vector space is required to obtain the orthonormal bases, whereas relative to these bases, the calculations are considerably simplified. In a Euclidean vector space, scalar product can be used to define the length of vectors and the angle between them.
George A. Anastassiou, Iuliana F. Iatan
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The study of the Euclidean vector space is required to obtain the orthonormal bases, whereas relative to these bases, the calculations are considerably simplified. In a Euclidean vector space, scalar product can be used to define the length of vectors and the angle between them.
George A. Anastassiou, Iuliana F. Iatan
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2018
When dealing with vectors of \(\mathcal{V}_O^3\) in Chap. 1, we have somehow implicitly used the notions of length for a vector and of orthogonality of vectors as well as amplitude of plane angle between vectors. In order to generalise all of this, in the present chapter we introduce the structure of scalar product for any vector space, thus coming to ...
Giovanni Landi, Alessandro Zampini
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When dealing with vectors of \(\mathcal{V}_O^3\) in Chap. 1, we have somehow implicitly used the notions of length for a vector and of orthogonality of vectors as well as amplitude of plane angle between vectors. In order to generalise all of this, in the present chapter we introduce the structure of scalar product for any vector space, thus coming to ...
Giovanni Landi, Alessandro Zampini
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Mathematical Proceedings of the Cambridge Philosophical Society, 1987
R denotes the set of real numbers. For any finite n, Rn denotes n-dimensional space with the usual (Hilbert space) metric, d.
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R denotes the set of real numbers. For any finite n, Rn denotes n-dimensional space with the usual (Hilbert space) metric, d.
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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Cosmology with the Laser Interferometer Space Antenna
Living Reviews in Relativity, 2023Germano Nardini
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