作者Malkuth (Asgard)
看板Math
标题Re: [线代] 求对角矩阵
时间Wed Jun 22 20:02:18 2011
※ 引述《mqazz1 (无法显示)》之铭言：
: [ a b c ]
: A = [ d e f ]
: [ g h i ]
: [ a 1/2b 1/4c ]
: D^(-1) A D = [ 2d e 1/2f ]
: [ 4g 2h i ]
: D is diagonal matrix
: 求 D = ?
: 请问这题要怎麽求呢?
: 谢谢
[x 0 0] [1/x 0 0 ]
假设D=[0 y 0] ，则D^(-1)=[0 1/y 0 ]
[0 0 z] [0 0 1/z ]
[1/x 0 0 ] [ax by cz] [a by/x cz/x]
D^(-1) A D = [0 1/y 0 ] [dx ey fz] = [dx/y e fz/y]
[0 0 1/z ] [gx hy iz] [gx/z hy/z i ]
x:y:z=4:2:1
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