Minors

[Robert M. Mazo]

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
ma...@uoregon.edu

[Caffa Vittorio Dr.]

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
ca...@iabg.de