| [ KAIST ] in KIDS 글 쓴 이(By): guest (cortex) <0-1pool99-170.na> 날 짜 (Date): 2002년 8월 11일 일요일 오후 01시 08분 54초 제 목(Title): matrix products there are many ways to define higher dimensional matrix products. the most well known product is called Kroneker product. let A=(a_ij) B= (b_ij) Then A * B = (a_ijB) this operation increase the dim(A*B) = dim(A)*dim(B) hence it can be used in defining 3D matrix algebra. matlab has this operator defined. you don't need levi-chita or something to compute determinant. look at Shaum's outline series on linear algebra. :) it's just permutation signs. + permutation gets 1 - permutation gets -1. (you don't want to look at Afken for linear algebra). however if A = B + I, then there is a very interesting formula for det. you can actually expand det to be det (B+I) = 1 + tr(B) + detr_1 (B) + detr_2(B) + .... i am suer you can find out what detr is in marix theory books. probably the best matrix theory book i can rcommand is by Horns if i got the spelling correct. also for block matrix, det can be decomposed into det of submatrix. there is a certain name for this formula called Shur's compliment or soemthing. don't use tensors in matrix if you are not actually programming some matrix algebra. tenros are highly unintuitive and should be avoided if necesssary. only newbis on tensors tend to advertise them. :) |