. . . . . . . . "vec\u4F5C\u7528\u7D20\uFF08\u82F1\u8A9E: vec operator\uFF09\u3068\u306F m \u00D7 n \u884C\u5217 A \u306E\u8981\u7D20\u3092 mn \u6B21\u5143\u5217\u30D9\u30AF\u30C8\u30EB\u306E\u5F62\u306B\u914D\u7F6E\u3057\u76F4\u3059\u4F5C\u7528\u7D20\u3067\u3042\u308B\u3002vec\u4F5C\u7528\u7D20\u306F\u884C\u5217\u306E\u5FAE\u5206\u3092\u884C\u3046\u306E\u306B\u4FBF\u5229\u306A\u3053\u3068\u304C\u3042\u308B\u3002 m \u00D7 n \u884C\u5217 A \u3092 m \u6B21\u5143\u5217\u30D9\u30AF\u30C8\u30EB \u3092\u7528\u3044\u3066 \u3068\u66F8\u3051\u308B\u3068\u304D\u3001 \u3068\u3057\u3066\u5B9A\u7FA9\u3055\u308C\u308B\u3002"@ja . . . . . . . . "\uBCA1\uD130\uD654"@ko . . . . . . . . "\uC218\uD559\uC5D0\uC11C, \uD2B9\uD788 \uC120\uD615\uB300\uC218\uD559\uACFC \uD589\uB82C \uC774\uB860\uC5D0\uC11C \uD589\uB82C\uC758 \uBCA1\uD130\uD654(Vector\u5316, \uC601\uC5B4:Vectorization)\uB294 \uD589\uB82C\uC744 \uC138\uB85C \uBCA1\uD130\uB85C \uBC14\uAFB8\uB294 \uC120\uD615\uBCC0\uD658\uC758 \uD558\uB098\uC774\uB2E4. m\u00D7n\uD589\uB82C A\uC758 \uC120\uD615\uD654\uB294 vec(A)\uB85C \uD45C\uAE30\uD558\uBA70, \uD589\uB82C A\uC758 \uC5F4\uC744 \uB2E4\uC74C \uC5F4 \uC704\uC5D0 \uC313\uC544\uAC00\uBA70 \uC5BB\uC744 \uC218 \uC788\uB2E4. \uB294 \uD589\uB82C \uC758 \uC131\uBD84\uC744 \uB098\uD0C0\uB0B4\uBA70, \uB294 \uC804\uCE58\uD589\uB82C\uC744 \uB098\uD0C0\uB0B8\uB2E4. \uBCA1\uD130\uD654\uB294 (\uD589\uB82C\uACFC \uBCA1\uD130\uC758)\uBCA1\uD130 \uACF5\uAC04 \uC0AC\uC774\uC758 \uB3D9\uD615 \uC0AC\uC0C1 \uC744 \uB098\uD0C0\uB0B8\uB2E4. \uC608\uB97C \uB4E4\uC5B4, 2\u00D72 \uD589\uB82C = \uB97C \uBCA1\uD130\uD654\uD558\uBA74\uAC00 \uB41C\uB2E4."@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 \u00D7 n matrix A, denoted vec(A), is the mn \u00D7 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\u00D72 matrix , the vectorization is ."@en . . . . . . "\uC218\uD559\uC5D0\uC11C, \uD2B9\uD788 \uC120\uD615\uB300\uC218\uD559\uACFC \uD589\uB82C \uC774\uB860\uC5D0\uC11C \uD589\uB82C\uC758 \uBCA1\uD130\uD654(Vector\u5316, \uC601\uC5B4:Vectorization)\uB294 \uD589\uB82C\uC744 \uC138\uB85C \uBCA1\uD130\uB85C \uBC14\uAFB8\uB294 \uC120\uD615\uBCC0\uD658\uC758 \uD558\uB098\uC774\uB2E4. m\u00D7n\uD589\uB82C A\uC758 \uC120\uD615\uD654\uB294 vec(A)\uB85C \uD45C\uAE30\uD558\uBA70, \uD589\uB82C A\uC758 \uC5F4\uC744 \uB2E4\uC74C \uC5F4 \uC704\uC5D0 \uC313\uC544\uAC00\uBA70 \uC5BB\uC744 \uC218 \uC788\uB2E4. \uB294 \uD589\uB82C \uC758 \uC131\uBD84\uC744 \uB098\uD0C0\uB0B4\uBA70, \uB294 \uC804\uCE58\uD589\uB82C\uC744 \uB098\uD0C0\uB0B8\uB2E4. \uBCA1\uD130\uD654\uB294 (\uD589\uB82C\uACFC \uBCA1\uD130\uC758)\uBCA1\uD130 \uACF5\uAC04 \uC0AC\uC774\uC758 \uB3D9\uD615 \uC0AC\uC0C1 \uC744 \uB098\uD0C0\uB0B8\uB2E4. \uC608\uB97C \uB4E4\uC5B4, 2\u00D72 \uD589\uB82C = \uB97C \uBCA1\uD130\uD654\uD558\uBA74\uAC00 \uB41C\uB2E4."@ko . . . . . . . . . . "7136985"^^ . . "Vectorization (mathematics)"@en . . . . . . "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 \u00D7 n matrix A, denoted vec(A), is the mn \u00D7 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\u00D72 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\u4F5C\u7528\u7D20\uFF08\u82F1\u8A9E: vec operator\uFF09\u3068\u306F m \u00D7 n \u884C\u5217 A \u306E\u8981\u7D20\u3092 mn \u6B21\u5143\u5217\u30D9\u30AF\u30C8\u30EB\u306E\u5F62\u306B\u914D\u7F6E\u3057\u76F4\u3059\u4F5C\u7528\u7D20\u3067\u3042\u308B\u3002vec\u4F5C\u7528\u7D20\u306F\u884C\u5217\u306E\u5FAE\u5206\u3092\u884C\u3046\u306E\u306B\u4FBF\u5229\u306A\u3053\u3068\u304C\u3042\u308B\u3002 m \u00D7 n \u884C\u5217 A \u3092 m \u6B21\u5143\u5217\u30D9\u30AF\u30C8\u30EB \u3092\u7528\u3044\u3066 \u3068\u66F8\u3051\u308B\u3068\u304D\u3001 \u3068\u3057\u3066\u5B9A\u7FA9\u3055\u308C\u308B\u3002"@ja . . . . . . . . "Vec\u4F5C\u7528\u7D20"@ja . . "8825"^^ . . . . . . "1095754114"^^ . . . . .