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相对论、量子力学及其场论的,本质、规律,及其必然且必需的发展(35)
时空可变系推广到任意n维的多线矢。
(接(34))
[可变基矢系(X)] =[矩阵C((X)(A))] [不变基矢系(A)]; 并有:
[不变基矢系(A)]= [矩阵C((A)(X))] [可变基矢系(X)], 即:
[基矢(X)((x))]=[C((X)(A)((x)(a))) [基矢(A)((a))],(a)=(a)1到(a)n], (x)=(x)1到(x)n;
[基矢(A)((a))]=[C((A)(X) ((a)(x))) [基矢(X)((x))], (x)=(x)1到(x)n], (a)=(a)1到(a)n,
C((X)(A)((x)(a))), C((A)(X) ((a)(x)))分别是n维多线矢矩阵[矩阵C((X)(A))],[矩阵C((A)(X))]的各相应矩阵元,它们都是两参考系间的偏转情况。并有:
[C((X)(A)((x)(a))) C((A)(X)((a)(x’))), (a)=(a)1到(a)n求和]=1((x)=(x’));
=0((x)不=(x’))。
[矩阵C(XA)],[矩阵C(AX)]互为转置逆矩阵,具体表达[可变基矢系X]、[不变基矢系A]间的偏转情况。
[矢(A)((X))] =[(A)((X),(x))[[基矢(X)((x))], (x)=(x)1到(x)n求和]
=[矢(A)((A))]=[(A)((A),(a))[[基矢(A)((a))], (a)=(a)1到(a)n求和],
(A)((X),(x)) =[C((X)(A),(x)(a))(A)((A),(a)), (a)=(a)1到(a)n求和], (x)=(x)1到(x)n,
(A)((A),(a)) =[C((A)(X),(( a)(x))(A)((X),(x)), (x)=(x)1到(x)n求和], (a)=(a)1到(a)n,
(未完待续)
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