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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