IEC 60050 - International Electrotechnical Vocabulary


IEVref:	102-03-08		ID:
Language:	en		Status: Obsolete

Term:	base
Synonym1:	basis [Preferred]
Synonym2:
Synonym3:
Symbol:
Definition:	ordered set of n linearly independent vectors $a_{1}, a_{2}, ..., a_{n}$ in an n-dimensional vector space, which is chosen to express any vector U as a unique linear combination of these n vectors: $U = U_{1} a_{1} + U_{2} a_{2} + ... + U_{n} a_{n}$ , where $U_{1}, U_{2}, ..., U_{n}$ are scalars NOTE 1 In an Euclidean or Hermitian vector space, an orthonormal base is generally chosen. In the vector space formed by a set of n-bit words (see Note of entry "vector space") a base is the set of n-bit words having only one non-zero bit. NOTE 2 Any vector of a base is called "base vector".
Publication date:	2007-08
Source
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Internal notes:	2017-06-02: Cleanup - Remove Attached Image 102-03-08en.gif
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n a 1 , a 2 , ..., a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahggadaWgaaWcba acbaqcLboacaWFXaaaleqaaOGaaeilaiaaysW7caWHHbWaaSbaaSqa aKqzGdGaa8NmaaWcbeaakiaabYcacaaMe8UaaeOlaiaab6cacaqGUa GaaeilaiaaysW7caWHHbWaaSbaaSqaaiaad6gaaeqaaaaa@49FD@ nUn U= U 1 a 1 + U 2 a 2 +...+ U n a n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfacqGH9aqpca WGvbWaaSbaaSqaaGqaaKqzGdGaa8xmaaWcbeaakiaahggadaWgaaWc baqcLboacaWFXaaaleqaaOGaey4kaSIaamyvamaaBaaaleaajug4ai aa=jdaaSqabaGccaWHHbWaaSbaaSqaaKqzGdGaa8NmaaWcbeaakiab gUcaRiaac6cacaGGUaGaaiOlaiabgUcaRiaadwfadaWgaaWcbaGaam OBaaqabaGccaWHHbWaaSbaaSqaaiaad6gaaeqaaaaa@5010@ U 1 , U 2 , ..., U n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadwfadaWgaaWcba acbaqcLboacaWFXaaaleqaaOGaaeilaiaaysW7caWGvbWaaSbaaSqa aKqzGdGaa8NmaaWcbeaakiaabYcacaaMe8UaaeOlaiaab6cacaqGUa GaaeilaiaaysW7caWGvbWaaSbaaSqaaiaad6gaaeqaaaaa@49CD@ NOTE 1 In an Euclidean or Hermitian vector space, an orthonormal base is generally chosen. In the vector space formed by a set of n-bit words (see Note of entry "vector space") a base is the set of n-bit words having only one non-zero bit. NOTE 2 Any vector of a base is called "base vector".