Ah... message is gone, so I write again. OTL...
I solve the Linear Algebra course problems on Sage. Now I get the nullity of matrix to use nullity function, but it's weird. If I get the nullity of matrix A to use nullity function like that, A.nullity() but the result of this is same as left nullity of A. So rank + nullity is not columns of A. According to the Rank-Nullity Theorem, rank A + nullity A = number of columns of A. It's weird. So I read the source file. On SAGEROOT/devel/sage/sage/matrix/matrix2.pyx line 1546, (ver 3.4.1) nullity = left_nullity and definition of left_nullity function's comments # Use that rank + nullity = number of rows, since matrices act # from the right on row vectors. But left null space of A is same as null space of transpose A. http://en.wikipedia.org/wiki/Null_space#Left_null_space So I think it is wrong, I modified the code like that. nullity = left_nullity => nullity = right_nullity The result of this is here. http://121.169.55.178:8000/home/pub/2/ (It's my desktop computer, so it's slow.) Nullity function's document is here. http://www.sagemath.org/doc/reference/sage/matrix/matrix2.html#sage.matrix.matrix2.Matrix.nullity It said this function return the left nullity of matrix. Is it wrong, or right? ------------------------------------------------------------------------ 누구나가 다, 자기 옆에서 눈물을 흘리며 신음하는 불행한 사람들에 비해 자기가 훨씬 더 불행하다고 생각하지요. 이게 바로 우리 가련한 인간들의 오만 중의 하나입니다. - 몬테크리스토 백작 it is the infirmity of our nature always to believe ourselves much more unhappy than those who groan by our sides! - The Count of Monte Cristo c'est un des orgueils de notre pauvre humanité, que chaque homme se croie plus malheureux qu'un autre malheureux qui pleure et qui gémit à côté de lui - Le Comte de Monte-Cristo 박진영 - Bak Jin Yeong 학부재학생 - Undergraduate 컴퓨터공학전공 - Department of Computer Engineering 정보통신공학부 - School of Information & Communication Engineering 성균관대학교 - SungKyunKwan University 블로그 - http://nosyu.pe.kr 이메일 - don...@skku.edu --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
