DLMF:1.3.E13 (Q73): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10763 / rank
 
Normal rank
Property / Symbols used: Q10763 / qualifier
 
Defining formula:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q10763 / qualifier
 
xml-id: C1.S1.XMD3.m1kdec

Revision as of 15:49, 1 January 2020

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English
DLMF:1.3.E13
No description defined

    Statements

    Defining formula
    | 1 x 1 x 1 2 ⋯ x 1 n - 1 1 x 2 x 2 2 ⋯ x 2 n - 1 ⋮ ⋮ ⋮ ⋱ ⋮ 1 x n x n 2 ⋯ x n n - 1 | = ∏ 1 ≤ j < k ≤ n ( x k - x j ) . 1 subscript 𝑥 1 subscript superscript 𝑥 2 1 ⋯ subscript superscript 𝑥 𝑛 1 1 1 subscript 𝑥 2 subscript superscript 𝑥 2 2 ⋯ subscript superscript 𝑥 𝑛 1 2 ⋮ ⋮ ⋮ ⋱ ⋮ 1 subscript 𝑥 𝑛 subscript superscript 𝑥 2 𝑛 ⋯ superscript subscript 𝑥 𝑛 𝑛 1 subscript product 1 𝑗 𝑘 𝑛 subscript 𝑥 𝑘 subscript 𝑥 𝑗 {\displaystyle{\displaystyle\begin{vmatrix}1&x_{1}&x^{2}_{1}&\cdots&x^{n-1}_{1% }\\ 1&x_{2}&x^{2}_{2}&\cdots&x^{n-1}_{2}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ 1&x_{n}&x^{2}_{n}&\cdots&x_{n}^{n-1}\end{vmatrix}=\prod_{1\leq j<k\leq n}(x_{k% }-x_{j}).}}
    0 references
    DLMF id
    DLMF:1.3.E13
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q10765
    Defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1ajdec
    0 references
    Q10763
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C1.S1.XMD3.m1kdec
    0 references
     
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