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d=det(aij)大学行列式.求解
d=det(aij)其中aij=(德尔塔小写ij)-xixj/x”2
x”=(x1,x2...xn)不等于0
人气:296 ℃ 时间:2020-06-12 02:26:29
解答
xixj/x”2
x”=(x1,x2...xn)不等于0|x|^2=x1^2+x2^2+...+xn^2
D=
1-x1^2/|x|^2-x1x2/|x|^2 ... -x1xn/|x|^2
-x2x1/|x|^2 1-x2^2/|x|^2 ... -x2xn/|x|^2
....
-xnx1/|x|^2-xnx2/|x|^2 ... 1-xn^2/|x|^2
加边
1 x1/|x|^2 x2/|x|^2 ...xn/|x|^2
0 1-x1^2/|x|^2-x1x2/|x|^2 ... -x1xn/|x|^2
0-x2x1/|x|^2 1-x2^2/|x|^2 ... -x2xn/|x|^2
....
0-xnx1/|x|^2-xnx2/|x|^2 ... 1-xn^2/|x|^2

ri + xi-1r1, i=2,3,...,n+1
1 x1/|x|^2 x2/|x|^2 ... xn/|x|^2
x110 ... 0
x201 ... 0
...
xn00 ... 1

c1-x1c2-x2c3-...-xncn+1
1-x1^2/|x|^2-...-xn^2/|x|^2x1/|x|^2 x2/|x|^2 ... xn/|x|^2
010 ... 0
001 ... 0
...
000 ... 1
=
0x1/|x|^2 x2/|x|^2 ... xn/|x|^2
010 ... 0
001 ... 0
...
000 ... 1

= 0
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