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- Normed_vector_space abstract "In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of "vector length" are crucial.1. The zero vector, 0, has zero length; every other vector has a positive length.if 2. Multiplying a vector by a positive number changes its length without changing its direction. Moreover,for any scalar 3. The triangle inequality holds. That is, taking norms as distances, the distance from point A through B to C is never shorter than going directly from A to C, or the shortest distance between any two points is a straight line.for any vectors x and y. (triangle inequality)The generalization of these three properties to more abstract vector spaces leads to the notion of norm. A vector space on which a norm is defined is then called a normed vector space.Normed vector spaces are central to the study of linear algebra and functional analysis.".
- Normed_vector_space wikiPageID "21538".
- Normed_vector_space wikiPageRevisionID "600872844".
- Normed_vector_space hasPhotoCollection Normed_vector_space.
- Normed_vector_space subject Category:Normed_spaces.
- Normed_vector_space type Abstraction100002137.
- Normed_vector_space type Attribute100024264.
- Normed_vector_space type NormedSpaces.
- Normed_vector_space type Space100028651.
- Normed_vector_space comment "In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of "vector length" are crucial.1. The zero vector, 0, has zero length; every other vector has a positive length.if 2. Multiplying a vector by a positive number changes its length without changing its direction. Moreover,for any scalar 3. The triangle inequality holds.".
- Normed_vector_space label "Espace vectoriel normé".
- Normed_vector_space label "Espacio vectorial normado".
- Normed_vector_space label "Espaço normado".
- Normed_vector_space label "Genormeerde vectorruimte".
- Normed_vector_space label "Normed vector space".
- Normed_vector_space label "Normierter Raum".
- Normed_vector_space label "Przestrzeń unormowana".
- Normed_vector_space label "Spazio normato".
- Normed_vector_space label "Нормированное пространство".
- Normed_vector_space label "فضاء متجهي معياري".
- Normed_vector_space label "ノルム線型空間".
- Normed_vector_space label "賦範向量空間".
- Normed_vector_space sameAs Normierter_Raum.
- Normed_vector_space sameAs Espacio_vectorial_normado.
- Normed_vector_space sameAs Espace_vectoriel_normé.
- Normed_vector_space sameAs Spazio_normato.
- Normed_vector_space sameAs ノルム線型空間.
- Normed_vector_space sameAs Genormeerde_vectorruimte.
- Normed_vector_space sameAs Przestrzeń_unormowana.
- Normed_vector_space sameAs Espaço_normado.
- Normed_vector_space sameAs m.05dm4.
- Normed_vector_space sameAs Q726210.
- Normed_vector_space sameAs Q726210.
- Normed_vector_space sameAs Normed_vector_space.
- Normed_vector_space wasDerivedFrom Normed_vector_space?oldid=600872844.
- Normed_vector_space isPrimaryTopicOf Normed_vector_space.