反対角行列
n×nの反対角行列 A の行列要素 aj,k は数列 {di}(1≦i≦n)に対し次式で定まる。
a j , k = { 0 ( j + k ≠ n + 1 ) d j ( j + k = n + 1 ) {\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
( 0 0 0 ⋯ 0 0 d 1 0 0 ⋯ 0 0 d 2 0 0 ⋮ 0 0 d . . . 0 0 ⋮ 0 0 d i 0 0 ⋮ 0 0 d . . . 0 0 ⋮ 0 0 d n − 1 0 0 ⋯ 0 0 d n 0 0 ⋯ 0 0 0 ) {\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}}}