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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク immanant of a matrix ： ウィキペディア英語版 :''Immanant redirects here; it should not be confused with the philosophical immanent.''In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.Let \lambda=(\lambda_1,\lambda_2,\ldots) be a partition of n and let \chi_\lambda be the corresponding irreducible representation-theoretic character of the symmetric group S_n. The ''immanant'' of an n\times n matrix A=(a_) associated with the character \chi_\lambda is defined as the expression:_\lambda(A)=\sum_\chi_\lambda(\sigma)a_a_\cdots a_.The determinant is a special case of the immanant, where \chi_\lambda is the alternating character \sgn, of ''S'n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * :''Immanant redirects here; it should not be confused with the philosophical immanent.'' In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent. Let $\backslash lambda=(\backslash lambda\_1,\backslash lambda\_2,\backslash ldots)$ be a partition of $n$ and let $\backslash chi\_\backslash lambda$ be the corresponding irreducible representation-theoretic character of the symmetric group $S\_n$. The ''immanant'' of an $n\backslash times\; n$ matrix $A=(a\_)$ associated with the character $\backslash chi\_\backslash lambda$ is defined as the expression :$\_\backslash lambda(A)=\backslash sum\_\backslash chi\_\backslash lambda(\backslash sigma)a\_a\_\backslash cdots\; a\_.$ The determinant is a special case of the immanant, where $\backslash chi\_\backslash lambda$ is the alternating character $\backslash sgn$, of ''S''''n'', defined by the parity of a permutation. The permanent is the case where $\backslash chi\_\backslash lambda$ is the trivial character, which is identically equal to 1. For example, for $3\; \backslash times\; 3$ matrices, there are three irreducible representations of $S\_3$, as shown in the character table: As stated above, $\backslash chi\_1$ produces the permanent and $\backslash chi\_2$ produces the determinant, but $\backslash chi\_3$ produces the operation that maps as follows: : Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group. ==References== * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「:''Immanant redirects here; it should not be confused with the philosophical immanent.''In mathematics, the '''immanant of a matrix''' was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.Let \lambda=(\lambda_1,\lambda_2,\ldots) be a partition of n and let \chi_\lambda be the corresponding irreducible representation-theoretic character of the symmetric group S_n. The ''immanant'' of an n\times n matrix A=(a_) associated with the character \chi_\lambda is defined as the expression:_\lambda(A)=\sum_\chi_\lambda(\sigma)a_a_\cdots a_.The determinant is a special case of the immanant, where \chi_\lambda is the alternating character \sgn, of ''S''''n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * 」の詳細全文を読む n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * :''Immanant redirects here; it should not be confused with the philosophical immanent.'' In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent. Let $\backslash lambda=(\backslash lambda\_1,\backslash lambda\_2,\backslash ldots)$ be a partition of $n$ and let $\backslash chi\_\backslash lambda$ be the corresponding irreducible representation-theoretic character of the symmetric group $S\_n$. The ''immanant'' of an $n\backslash times\; n$ matrix $A=(a\_)$ associated with the character $\backslash chi\_\backslash lambda$ is defined as the expression :$\_\backslash lambda(A)=\backslash sum\_\backslash chi\_\backslash lambda(\backslash sigma)a\_a\_\backslash cdots\; a\_.$ The determinant is a special case of the immanant, where $\backslash chi\_\backslash lambda$ is the alternating character $\backslash sgn$, of ''S''''n'', defined by the parity of a permutation. The permanent is the case where $\backslash chi\_\backslash lambda$ is the trivial character, which is identically equal to 1. For example, for $3\; \backslash times\; 3$ matrices, there are three irreducible representations of $S\_3$, as shown in the character table: As stated above, $\backslash chi\_1$ produces the permanent and $\backslash chi\_2$ produces the determinant, but $\backslash chi\_3$ produces the operation that maps as follows: : Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group. ==References== * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「:''Immanant redirects here; it should not be confused with the philosophical immanent.''In mathematics, the '''immanant of a matrix''' was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.Let \lambda=(\lambda_1,\lambda_2,\ldots) be a partition of n and let \chi_\lambda be the corresponding irreducible representation-theoretic character of the symmetric group S_n. The ''immanant'' of an n\times n matrix A=(a_) associated with the character \chi_\lambda is defined as the expression:_\lambda(A)=\sum_\chi_\lambda(\sigma)a_a_\cdots a_.The determinant is a special case of the immanant, where \chi_\lambda is the alternating character \sgn, of ''S''''n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * 」の詳細全文を読む n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * ">ウィキペディア（Wikipedia）』 ■ウィキペディアで「:''Immanant redirects here; it should not be confused with the philosophical immanent.''In mathematics, the '''immanant of a matrix''' was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.Let \lambda=(\lambda_1,\lambda_2,\ldots) be a partition of n and let \chi_\lambda be the corresponding irreducible representation-theoretic character of the symmetric group S_n. The ''immanant'' of an n\times n matrix A=(a_) associated with the character \chi_\lambda is defined as the expression:_\lambda(A)=\sum_\chi_\lambda(\sigma)a_a_\cdots a_.The determinant is a special case of the immanant, where \chi_\lambda is the alternating character \sgn, of ''S''''n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * 」の詳細全文を読む n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * ">ウィキペディアで「:''Immanant redirects here; it should not be confused with the philosophical immanent.''In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.Let \lambda=(\lambda_1,\lambda_2,\ldots) be a partition of n and let \chi_\lambda be the corresponding irreducible representation-theoretic character of the symmetric group S_n. The ''immanant'' of an n\times n matrix A=(a_) associated with the character \chi_\lambda is defined as the expression:_\lambda(A)=\sum_\chi_\lambda(\sigma)a_a_\cdots a_.The determinant is a special case of the immanant, where \chi_\lambda is the alternating character \sgn, of ''S'n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * 」の詳細全文を読む n'', defined by the parity of a permutation.The permanent is the case where \chi_\lambda is the trivial character, which is identically equal to 1.For example, for 3 \times 3 matrices, there are three irreducible representations of S_3, as shown in the character table:As stated above, \chi_1 produces the permanent and \chi_2 produces the determinant, but \chi_3 produces the operation that maps as follows::\begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ a_ & a_ & a_ \end \rightsquigarrow 2 a_ a_ a_ - a_ a_ a_ - a_ a_ a_Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.==References==* * 」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. 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