“Vandermonde’s determinant”的概念、定义、翻译、参考文献-科学参考

Vandermonde’s determinant

Mathematics

For n real numbers x₁,x₂,…, x_n, the determinant

$| \begin{matrix} \begin{matrix} 1 & x_{1} \\ 1 & x_{2} \end{matrix} & \begin{matrix} x_{1}^{2} & \dots & x_{1}^{n - 1} \\ x_{2}^{2} & \dots & x_{2}^{n - 1} \end{matrix} \\ \begin{matrix} 1 & x_{3} \\ ⋮ & ⋮ \\ 1 & x_{n} \end{matrix} & \begin{matrix} x_{3}^{2} & \dots & x_{3}^{n - 1} \\ ⋮ & \dots & ⋮ \\ x_{n}^{2} & \dots & x_{n}^{n - 1} \end{matrix} \end{matrix} | = \prod_{i > j} (x_{i} - x_{j}) .$

Note that the determinant is non-zero, and so the matrix is invertible, if and only if the x_i are distinct.

单词	Vandermonde’s determinant
释义	Vandermonde’s determinant Mathematics For n real numbers x₁,x₂,…, x_n, the determinant $\| \begin{matrix} \begin{matrix} 1 & x_{1} \\ 1 & x_{2} \end{matrix} & \begin{matrix} x_{1}^{2} & \dots & x_{1}^{n - 1} \\ x_{2}^{2} & \dots & x_{2}^{n - 1} \end{matrix} \\ \begin{matrix} 1 & x_{3} \\ ⋮ & ⋮ \\ 1 & x_{n} \end{matrix} & \begin{matrix} x_{3}^{2} & \dots & x_{3}^{n - 1} \\ ⋮ & \dots & ⋮ \\ x_{n}^{2} & \dots & x_{n}^{n - 1} \end{matrix} \end{matrix} \| = \prod_{i > j} (x_{i} - x_{j}) .$ Note that the determinant is non-zero, and so the matrix is invertible, if and only if the x_i are distinct.
随便看	gross drying rate gross economic potential Grosseteste, Robert (c.1168–1253) gross fixed investment grossing up gross investment gross lift-off weight gross national income gross national product gross profit gross reproduction rate gross trading profit grossular gross value added Grothendieck, Alexander (1928–2014) Grotius, Hugo (1583–1645) Grotrian diagram Grotthuss–Draper law ground ground absorption ground anchor ground capacitance ground clutter Ground Communications Facilities ground control