| dbo:abstract |
In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a column vector. Specifically, the vectorization of a m × n matrix A, denoted vec(A), is the mn × 1 column vector obtained by stacking the columns of the matrix A on top of one another: Here, represents and the superscript denotes the transpose. Vectorization expresses, through coordinates, the isomorphism between these (i.e., of matrices and vectors) as vector spaces. For example, for the 2×2 matrix , the vectorization is . The connection between the vectorization of A and the vectorization of its transpose is given by the commutation matrix. (en) vec作用素（英語: vec operator）とは m × n 行列 A の要素を mn 次元列ベクトルの形に配置し直す作用素である。vec作用素は行列の微分を行うのに便利なことがある。 m × n 行列 A を m 次元列ベクトル を用いて と書けるとき、 として定義される。 (ja) 수학에서, 특히 선형대수학과 행렬 이론에서 행렬의 벡터화(Vector化, 영어:Vectorization)는 행렬을 세로 벡터로 바꾸는 선형변환의 하나이다. m×n행렬 A의 선형화는 vec(A)로 표기하며, 행렬 A의 열을 다음 열 위에 쌓아가며 얻을 수 있다. 는 행렬 의 성분을 나타내며, 는 전치행렬을 나타낸다. 벡터화는 (행렬과 벡터의)벡터 공간 사이의 동형 사상 을 나타낸다. 예를 들어, 2×2 행렬 = 를 벡터화하면가 된다. (ko) |
| dbo:thumbnail |
wiki-commons:Special:FilePath/Vectorized-addition.gif?width=300 |
| dbo:wikiPageID |
7136985 (xsd:integer) |
| dbo:wikiPageLength |
8825 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1095754114 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Python_(programming_language) dbr:Algebra_homomorphism dbr:Julia_(programming_language) dbr:Packed_storage_matrix dbr:Column_vector dbr:Complex_number dbr:Conjugate_transpose dbr:Mathematics dbr:Matlab dbr:Matrix_(mathematics) dbr:Matrix_multiplication dbr:Matrix_norm dbr:Symmetric_matrix dbr:GNU_Octave dbr:Lie_algebra dbr:Linear_algebra dbr:Commutation_matrix dbr:Identity_matrix dbr:Main_diagonal dbr:Matricization dbr:Adjoint_functors dbc:Matrices dbr:Transpose dbr:Hadamard_product_(matrices) dbc:Linear_algebra dbr:NumPy dbr:Hilbert–Schmidt_operator dbr:Isomorphism dbr:Duplication_matrix dbr:Unitary_transformation dbr:Inner_product dbr:Kronecker_product dbr:Voigt_notation dbr:Linear_transformation dbr:Row-major_order dbr:R_programming_language dbr:Elimination_matrix dbr:Lower_triangular_matrix dbr:Adjoint_endomorphism dbr:File:Vectorized-addition.gif |
| dbp:wikiPageUsesTemplate |
dbt:! dbt:Note_label dbt:Other_uses dbt:Ref_label dbt:Reflist dbt:Short_description dbt:Isbn |
| dct:subject |
dbc:Matrices dbc:Linear_algebra |
| rdf:type |
yago:WikicatMatrices yago:Abstraction100002137 yago:Arrangement107938773 yago:Array107939382 yago:Group100031264 yago:Matrix108267640 |
| rdfs:comment |
vec作用素（英語: vec operator）とは m × n 行列 A の要素を mn 次元列ベクトルの形に配置し直す作用素である。vec作用素は行列の微分を行うのに便利なことがある。 m × n 行列 A を m 次元列ベクトル を用いて と書けるとき、 として定義される。 (ja) 수학에서, 특히 선형대수학과 행렬 이론에서 행렬의 벡터화(Vector化, 영어:Vectorization)는 행렬을 세로 벡터로 바꾸는 선형변환의 하나이다. m×n행렬 A의 선형화는 vec(A)로 표기하며, 행렬 A의 열을 다음 열 위에 쌓아가며 얻을 수 있다. 는 행렬 의 성분을 나타내며, 는 전치행렬을 나타낸다. 벡터화는 (행렬과 벡터의)벡터 공간 사이의 동형 사상 을 나타낸다. 예를 들어, 2×2 행렬 = 를 벡터화하면가 된다. (ko) In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a column vector. Specifically, the vectorization of a m × n matrix A, denoted vec(A), is the mn × 1 column vector obtained by stacking the columns of the matrix A on top of one another: Here, represents and the superscript denotes the transpose. Vectorization expresses, through coordinates, the isomorphism between these (i.e., of matrices and vectors) as vector spaces. For example, for the 2×2 matrix , the vectorization is . (en) |
| rdfs:label |
Vec作用素 (ja) 벡터화 (ko) Vectorization (mathematics) (en) |
| owl:sameAs |
freebase:Vectorization (mathematics) yago-res:Vectorization (mathematics) wikidata:Vectorization (mathematics) dbpedia-ja:Vectorization (mathematics) dbpedia-ko:Vectorization (mathematics) https://global.dbpedia.org/id/4xsDK |
| prov:wasDerivedFrom |
wikipedia-en:Vectorization_(mathematics)?oldid=1095754114&ns=0 |
| foaf:depiction |
wiki-commons:Special:FilePath/Vectorized-addition.gif |
| foaf:isPrimaryTopicOf |
wikipedia-en:Vectorization_(mathematics) |
| is dbo:wikiPageDisambiguates of |
dbr:Vec dbr:Vectorization |
| is dbo:wikiPageRedirects of |
dbr:Vech dbr:Vectorization_(math) |
| is dbo:wikiPageWikiLink of |
dbr:Bayesian_multivariate_linear_regression dbr:Vector_(mathematics_and_physics) dbr:Duplication_and_elimination_matrices dbr:List_of_named_matrices dbr:Elliptical_distribution dbr:Low-rank_approximation dbr:Superoperator dbr:Quantum_Fisher_information dbr:Commutation_matrix dbr:Frobenius_inner_product dbr:Machine_learning_in_bioinformatics dbr:Matrix_normal_distribution dbr:Trace_(linear_algebra) dbr:A_Dynamical_Theory_of_the_Electromagnetic_Field dbr:Exponential_family dbr:Fang_Kaitai dbr:Stochastic_gradient_descent dbr:Inverse-Wishart_distribution dbr:Spatial_correlation dbr:Transportation_theory_(mathematics) dbr:Mode-k_flattening dbr:Bures_metric dbr:Kronecker_product dbr:Channel_state_information dbr:Lyapunov_equation dbr:Vec dbr:Vectorization dbr:Voigt_notation dbr:Outer_product dbr:Row-_and_column-major_order dbr:Sylvester_equation dbr:SAMV_(algorithm) dbr:Vector_autoregression dbr:Tensor_reshaping dbr:Vech dbr:Vectorization_(math) |
| is foaf:primaryTopic of |
wikipedia-en:Vectorization_(mathematics) |
