Dimension theorem for vector spaces
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite, or given by an infinite cardinal number, and defines the dimension of the space. Formally, the dimension theorem for vector spaces states that Given a vector space V, any two linearly independent generating sets (in other words, any two bases) have the same cardinality. If V is finitely generated, then it has a finite basis, and the result says that any two bases have the same number of elements.
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Dimension theorem for vector spaces
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite, or given by an infinite cardinal number, and defines the dimension of the space. Formally, the dimension theorem for vector spaces states that Given a vector space V, any two linearly independent generating sets (in other words, any two bases) have the same cardinality. If V is finitely generated, then it has a finite basis, and the result says that any two bases have the same number of elements.
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En mathématiques, le théorème ...... ni) commun à toutes ses bases.
@fr
In matematica, il teorema dell ...... a rispettivamente e . Allora .
@it
In mathematics, the dimension ...... e the same number of elements.
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Dimension theorem for vector spaces
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Teorema della dimensione per spazi vettoriali
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Théorème de la dimension pour les espaces vectoriels
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