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- Change_of_basis abstract "In linear algebra, a basis for a vector space of dimension n is a sequence of n vectors (α1, …, αn) with the property that every vector in the space can be expressed uniquely as a linear combination of the basis vectors. The matrix representations of operators are also determined by the chosen basis. Since it is often desirable to work with more than one basis for a vector space, it is of fundamental importance in linear algebra to be able to easily transform coordinate-wise representations of vectors and operators taken with respect to one basis to their equivalent representations with respect to another basis. Such a transformation is called a change of basis.Although the terminology of vector spaces is used below and the symbol R can be taken to mean the field of real numbers, the results discussed hold whenever R is a commutative ring and vector space is everywhere replaced with free R-module.".
- Change_of_basis thumbnail 3d_basis_transformation.svg?width=300.
- Change_of_basis wikiPageExternalLink lecture-31-change-of-basis-image-compression.
- Change_of_basis wikiPageExternalLink watch?v=1j5WnqwMdCk.
- Change_of_basis wikiPageID "1179451".
- Change_of_basis wikiPageRevisionID "600007090".
- Change_of_basis align "right".
- Change_of_basis caption "A linear combination of one basis set of vectors obtains new vectors . If they are linearly independent, these form a new basis set. The linear combinations relating the first set to the other extend to a linear transformation, called the change of basis.".
- Change_of_basis caption "A vector can be represented in two different bases .".
- Change_of_basis hasPhotoCollection Change_of_basis.
- Change_of_basis image "259200.0".
- Change_of_basis width "122".
- Change_of_basis width "290".
- Change_of_basis subject Category:Linear_algebra.
- Change_of_basis subject Category:Matrix_theory.
- Change_of_basis comment "In linear algebra, a basis for a vector space of dimension n is a sequence of n vectors (α1, …, αn) with the property that every vector in the space can be expressed uniquely as a linear combination of the basis vectors. The matrix representations of operators are also determined by the chosen basis.".
- Change_of_basis label "Basistransformatie".
- Change_of_basis label "Basiswechsel (Vektorraum)".
- Change_of_basis label "Change of basis".
- Change_of_basis label "Matrice de passage".
- Change_of_basis label "Matrice di cambiamento di base".
- Change_of_basis label "Матрица перехода".
- Change_of_basis label "基变更".
- Change_of_basis label "基底変換".
- Change_of_basis sameAs Matice_přechodu.
- Change_of_basis sameAs Basiswechsel_(Vektorraum).
- Change_of_basis sameAs Matrice_de_passage.
- Change_of_basis sameAs Matrice_di_cambiamento_di_base.
- Change_of_basis sameAs 基底変換.
- Change_of_basis sameAs Basistransformatie.
- Change_of_basis sameAs m.04dxx5.
- Change_of_basis sameAs Q810255.
- Change_of_basis sameAs Q810255.
- Change_of_basis wasDerivedFrom Change_of_basis?oldid=600007090.
- Change_of_basis depiction 3d_basis_transformation.svg.
- Change_of_basis isPrimaryTopicOf Change_of_basis.
