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2021
Abstract The first three sections of this chapter provide a thorough presentation of the concepts of basis and dimension. The approach is unified in the sense that it does not treat finite and infinite-dimensional spaces separately.
Rita Fioresi, Marta Morigi
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Abstract The first three sections of this chapter provide a thorough presentation of the concepts of basis and dimension. The approach is unified in the sense that it does not treat finite and infinite-dimensional spaces separately.
Rita Fioresi, Marta Morigi
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2017
In this chapter we discuss a wide range of basic topics related to vectors of real numbers. Some of the properties carry over to vectors over other fields, such as complex numbers, but the reader should not assume this. Occasionally, for emphasis, we will refer to “real” vectors or “real” vector spaces, but unless it is stated otherwise, we are ...
Garrett Birkhoff, Saunders Mac Lane
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In this chapter we discuss a wide range of basic topics related to vectors of real numbers. Some of the properties carry over to vectors over other fields, such as complex numbers, but the reader should not assume this. Occasionally, for emphasis, we will refer to “real” vectors or “real” vector spaces, but unless it is stated otherwise, we are ...
Garrett Birkhoff, Saunders Mac Lane
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1979
Throughout what follows a row vector a’ = (al,a2,…,an) is an ordered n-tuple of complex numbers ...
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Throughout what follows a row vector a’ = (al,a2,…,an) is an ordered n-tuple of complex numbers ...
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1978
In nearly all of the discussion to follow we shall deal with the set of real numbers. Occasionally, however, we shall deal with complex numbers as well. In order to avoid cumbersome repetition we shall denote the set we are dealing with by F and let the context elucidate whether we are speaking of real or complex numbers or both.
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In nearly all of the discussion to follow we shall deal with the set of real numbers. Occasionally, however, we shall deal with complex numbers as well. In order to avoid cumbersome repetition we shall denote the set we are dealing with by F and let the context elucidate whether we are speaking of real or complex numbers or both.
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
exaly