st: re: Stata's row and column labels for matrices

[Kit Baum <baum@bc.edu>]

Elmer said

"I note that Stata has some quirky results when reporting the 
contents=20
of matrices derived from operations involving transposes of other=20
matrices. I speak of the row and column markers. Watch carefully.

I create two matrices, A and B:

. matrix A =3D blah blah

. matrix B =3D blah blah

. matrix list A

A[2,3]
     c1  c2  c3
r1   1  -1   2
r2   0   3   4

. matrix list B

B[2,3]
     c1  c2  c3
r1   4   0  -3
r2  -1  -2   3

Everything's okay so far. Watch what happens when I ask for a product.

. matrix Q=3DA*B'

. matrix list Q

Q[2,2]
      r1   r2
r1   -2    7
r2  -12    6

Note how the column markers are defined.

There seems to be no consistency, too. Watch what happens when I=20
calculate another matrix:

. matrix R=3DA'*B

. matrix list R

R[3,3]
     c1  c2  c3
c1   4   0  -3
c2  -7  -6  12
c3   4  -8   6

Now, it's the row markers that have changed!"


I see nothing strange here. The first product (absent the DOS-inspired 
junk) has the number of rows of A and the number of columns of B'. 
Since the columns of B' are the rows of B, the result matrix should be 
labeled with the row names of A and the row names of B, which it is. 
Giving row and column names that include the matrix name make this 
clear:
. mat list A

A[2,3]
     ac1  ac2  ac3
ar1    1   -1    2
ar2    0    3    4

. mat list B

B[2,3]
     bc1  bc2  bc3
br1    4    0   -3
br2   -1   -2    3

. mat list C

C[2,2]
     br1  br2
ar1   -2    7
ar2  -12    6

Likewise, the rows of the product B' A should be labeled with the 
column names of B (which are the row names of B'), and the columns with 
the column names of A, which they are in a perfectly consistent 
fashion:

. mat list D

D[3,3]
     ac1  ac2  ac3
bc1    4   -7    4
bc2    0   -6   -8
bc3   -3   12    6

I fail to see anything unpredictable or arbitrary here. Stata matrices 
have named rows and columns, and those names propagate through the 
calculation in the same way that the numbers do. For instance,

symmetric eye[3,3]
       eyec1  eyec2  eyec3
eyer1      1
eyer2      0      1
eyer3      0      0      1

. mat E = D * eye

. mat list E

E[3,3]
     eyec1  eyec2  eyec3
bc1      4     -7      4
bc2      0     -6     -8
bc3     -3     12      6

This does not look quirky to me. If Stata did anything else with the 
names, it would.

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/