反対角行列

n×nの反対角行列 A の行列要素 a_j,k は数列 {d_i}(1≦i≦n)に対し次式で定まる。

${\displaystyle a_{j,k}={\begin{cases}0&(\,j+k\neq n+1\,)\\d_{j}&(\,j+k=n+1\,)\end{cases}}}$

ただし、1≦j≦n, 1≦k≦n

${\displaystyle {\begin{pmatrix}0&0&0&\cdots &0&0&d_{1}\\0&0&\cdots &0&0&d_{2}&0\\0&\vdots &0&0&d_{...}&0&0\\\vdots &0&0&d_{i}&0&0&\vdots \\0&0&d_{...}&0&0&\vdots &0\\0&d_{n-1}&0&0&\cdots &0&0\\d_{n}&0&0&\cdots &0&0&0\\\end{pmatrix}}}$

${\displaystyle {\begin{pmatrix}0&0&0&0&1\\0&0&0&7&0\\0&0&-2&0&0\\0&6&0&0&0\\8&0&0&0&0\\\end{pmatrix}}}$