Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Commutation_matrix> ?p ?o. }
Showing items 1 to 20 of
20
with 100 items per page.
- Commutation_matrix abstract "In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix K(m,n) is the mn × mn matrix which, for any m × n matrix A, transforms vec(A) into vec(AT):K(m,n) vec(A) = vec(AT) .Here vec(A) is the mn × 1 column vector obtain by stacking the columns of A on top of one another:vec(A) = [ A1,1, ..., Am,1, A1,2, ..., Am,2, ..., A1,n, ..., Am,n ]Twhere A = [Ai,j].The commutation matrix is a special type of permutation matrix, and is therefore orthogonal. It is also an involution and symmetric.The main use of the commutation matrix, and the source of its name, is to commute the Kronecker product: for every m × n matrix A and every r × q matrix B,K(r,m)(A B)K(n,q) = B A.An explicit form for the commutation matrix is as follows: if er,j denotes the j-th canonical vector of dimension r (i.e. the vector with 1 in the j-th coordinate and 0 elsewhere) then K(r,m) = er,iem,jTem,jer,iT.".
- Commutation_matrix wikiPageID "7133473".
- Commutation_matrix wikiPageRevisionID "586505684".
- Commutation_matrix hasPhotoCollection Commutation_matrix.
- Commutation_matrix subject Category:Linear_algebra.
- Commutation_matrix subject Category:Matrices.
- Commutation_matrix type Abstraction100002137.
- Commutation_matrix type Arrangement107938773.
- Commutation_matrix type Array107939382.
- Commutation_matrix type Group100031264.
- Commutation_matrix type Matrices.
- Commutation_matrix type Matrix108267640.
- Commutation_matrix comment "In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose.".
- Commutation_matrix label "Commutation matrix".
- Commutation_matrix sameAs m.0h5xsy.
- Commutation_matrix sameAs Q5155088.
- Commutation_matrix sameAs Q5155088.
- Commutation_matrix sameAs Commutation_matrix.
- Commutation_matrix wasDerivedFrom Commutation_matrix?oldid=586505684.
- Commutation_matrix isPrimaryTopicOf Commutation_matrix.