Re: Minors
- To: mathgroup at smc.vnet.net
- Subject: [mg53030] Re: [mg52844] Minors
- From: "Caffa Vittorio Dr." <Caffa at iabg.de>
- Date: Mon, 20 Dec 2004 06:35:06 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
The notebook SymbolicFAQ.nb from the Information Center contains an interesting article called "Minors vs. cofactors" which gives a better answer to the original question. Here is the link: http://library.wolfram.com/infocenter/Conferences/325/ Cheers, Vittorio --- Vittorio G. Caffa caffa at iabg.de -----Original Message----- From: Caffa Vittorio Dr. [mailto:Caffa at iabg.de] To: mathgroup at smc.vnet.net Subject: [mg53030] [mg52918] Re: [mg52844] Minors Minors can be used to get all possible submatrices of a given matrix: In[1]:= a = Table[10i+j, {i,4}, {j,4}] Out[1]= {{11, 12, 13, 14}, {21, 22, 23, 24}, {31, 32, 33, 34}, {41, 42, 43, 44}} In[2]:= TableForm[a] Out[2]//TableForm= 11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44 In[3]:= Minors[a, 1, Identity] // TableForm Out[3]//TableForm= 11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44 In[4]:= Minors[a, 2, Identity] // TableForm Out[4]//TableForm= 11 12 11 13 11 14 12 13 12 14 13 14 21 22 21 23 21 24 22 23 22 24 23 24 11 12 11 13 11 14 12 13 12 14 13 14 31 32 31 33 31 34 32 33 32 34 33 34 11 12 11 13 11 14 12 13 12 14 13 14 41 42 41 43 41 44 42 43 42 44 43 44 21 22 21 23 21 24 22 23 22 24 23 24 31 32 31 33 31 34 32 33 32 34 33 34 21 22 21 23 21 24 22 23 22 24 23 24 41 42 41 43 41 44 42 43 42 44 43 44 31 32 31 33 31 34 32 33 32 34 33 34 41 42 41 43 41 44 42 43 42 44 43 44 In[5]:= Minors[a, 3, Identity] // TableForm Out[5]//TableForm= 11 12 13 11 12 14 11 13 14 12 13 14 21 22 23 21 22 24 21 23 24 22 23 24 31 32 33 31 32 34 31 33 34 32 33 34 11 12 13 11 12 14 11 13 14 12 13 14 21 22 23 21 22 24 21 23 24 22 23 24 41 42 43 41 42 44 41 43 44 42 43 44 11 12 13 11 12 14 11 13 14 12 13 14 31 32 33 31 32 34 31 33 34 32 33 34 41 42 43 41 42 44 41 43 44 42 43 44 21 22 23 21 22 24 21 23 24 22 23 24 31 32 33 31 32 34 31 33 34 32 33 34 41 42 43 41 42 44 41 43 44 42 43 44 In[6]:= Minors[a, 4, Identity] // TableForm Out[6]//TableForm= 11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44 Cheers, Vittorio --- Vittorio G. Caffa caffa at iabg.de -----Original Message----- From: Robert M. Mazo [mailto:mazo at uoregon.edu] To: mathgroup at smc.vnet.net Subject: [mg53030] [mg52918] [mg52844] Minors The Minors command gives, as the (i,j) minor af an nxn matrix, what ordinary mathematical notation calls the (n-i+1,n-j+1) minor . I know how to work around this. It is explained on pg. 1195 of The Mathematica Book (version 4). My question here is, why did the programmers of Mathematica define Minors this unconventional way? They usually had a good reason for their programming quirks, but I can't think of a reason for this one. Can anyone enlighten me? Robert Mazo mazo at uoregon.edu