数学のブログ

行列と双線形写像 双1次形式 座標の変換、基底、転置行列

ラング線形代数学(下) (ちくま学芸文庫) (S.ラング(著)、芹沢 正三(翻訳)、筑摩書房)の8章(行列と双線形写像)、1(双1次形式)、練習問題2の解答を求めてみる。

i d ( [ 1 1 0 ] ) = a 11 [ 1 0 0 ] + a 21 [ 0 1 0 ] + a 31 [ 0 0 1 ]
a 11 = 1 a 21 = 1 a 31 = 0
i d ( [ 0 1 0 ] ) = a 12 [ 1 0 0 ] + a 22 [ 0 1 0 ] + a 32 [ 0 0 1 ]
a 12 = 0 a 22 = 1 a 32 = 0
i d ( [ 1 1 1 ] ) = a 13 [ 1 0 0 ] + a 23 [ 0 1 0 ] + a 33 [ 0 0 1 ]
a 13 = 1 a 23 = 1 a 33 = 1
N = [ 1 0 1 1 1 1 0 0 1 ]
N T [ 1 2 3 - 1 1 1 1 0 1 ] N
= [ 1 1 0 0 1 0 1 1 1 ] [ 1 2 3 - 1 1 1 1 0 1 ] N
= [ 0 3 4 - 1 1 1 1 3 5 ] [ 1 0 1 1 1 1 0 0 1 ]
= [ 3 3 7 0 1 1 4 3 9 ]