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- Rank_factorization abstract "Given an matrix of rank , a rank decomposition or rank factorization of is a product , where is an matrix and is an matrix.Every finite-dimensional matrix has a rank decomposition: Let be an matrix whose column rank is . Therefore, there are linearly independent columns in equivalently, the dimension of the column space of is . Let be any basis for the column space of and place them as column vectors to form the matrix . Therefore, every column vector of is a linear combination of the columns of . To be precise, if is an matrix with as the -th column, thenwhere 's are the scalar coefficients of in terms of the basis . This implies that , where is the -th element of .".
- Rank_factorization wikiPageID "24920134".
- Rank_factorization wikiPageRevisionID "598779922".
- Rank_factorization hasPhotoCollection Rank_factorization.
- Rank_factorization subject Category:Linear_algebra.
- Rank_factorization subject Category:Matrix_decompositions.
- Rank_factorization type Abstraction100002137.
- Rank_factorization type Algebra106012726.
- Rank_factorization type Cognition100023271.
- Rank_factorization type Content105809192.
- Rank_factorization type Decomposition106013471.
- Rank_factorization type Discipline105996646.
- Rank_factorization type KnowledgeDomain105999266.
- Rank_factorization type Mathematics106000644.
- Rank_factorization type MatrixDecompositions.
- Rank_factorization type PsychologicalFeature100023100.
- Rank_factorization type PureMathematics106003682.
- Rank_factorization type Science105999797.
- Rank_factorization type VectorAlgebra106013298.
- Rank_factorization comment "Given an matrix of rank , a rank decomposition or rank factorization of is a product , where is an matrix and is an matrix.Every finite-dimensional matrix has a rank decomposition: Let be an matrix whose column rank is . Therefore, there are linearly independent columns in equivalently, the dimension of the column space of is . Let be any basis for the column space of and place them as column vectors to form the matrix .".
- Rank_factorization label "Factorización de rango".
- Rank_factorization label "Rank factorization".
- Rank_factorization label "階数因数分解".
- Rank_factorization sameAs Factorización_de_rango.
- Rank_factorization sameAs 階数因数分解.
- Rank_factorization sameAs m.09g772x.
- Rank_factorization sameAs Q7293212.
- Rank_factorization sameAs Q7293212.
- Rank_factorization sameAs Rank_factorization.
- Rank_factorization wasDerivedFrom Rank_factorization?oldid=598779922.
- Rank_factorization isPrimaryTopicOf Rank_factorization.