One approach I have used in this regard is to ask questions based on (Gasp!) reality:
- Perform a database query that is supposed to return a matrix with 3 columns (name, address, and phone number), and as many rows as meet the query criteria. Now, perform a query for some names that don't exist. What is the shape of the result? Clearly, it has to be 0x3. - Create a matrix of student test scores, one row per student, and one column per test. What is the shape of the array at the beginning of the semester? I have less trouble with "row vector" and "column vector", as those terms can be considered synonyms for the 1xN and Nx1 matrices. I agree that it's sloppy terminology. Bob On Sun, 2007-10-07 at 23:01 -0400, Devon McCormick wrote: > I find the APL/J general use of "arrays" and what they are to be simple, > useful, and consistent. > I agree with Ralph that calling a 1xN matrix a row vector and an Nx1 matrix > a column vector is, > at least, sloppy language. > > As for zero dimensions, they are completely consistent and unremarkable. If > you drop two rows from a > 2x2 matrix, what is the resulting shape? If you drop two columns > from a 2x2 matrix, what is the resulting > shape? > > I believe Ken used to explain it more finely by asking this question in > small steps, e.g. > Q: If you start with a 3x3 table, then remove one row, what is the new shape > of the table? (A: 2x3) > Q: If you remove another row from the result of the preceding step, what is > the new shape? (A: 1x3) > Q: If you remove another row from the result of the preceding step, what is > the new shape? (A: 0x3) > > > On 10/7/07, Raul Miller <[EMAIL PROTECTED]> wrote: > > > > On 10/7/07, Ralph G Selfridge <[EMAIL PROTECTED]> wrote: > > > We should be careful of using 'historic' reasons. Have you ever tried to > > > convince a mathematican that matrix multiplication (+/ .*) can be on > > other > > > than rank 2? And some time ago I had an argument that there are no such > > > things as a row vector or a column vector, a vector is a vector is a > > > vector. Row and column vectors are just ways of talking about a matrix > > with > > > a 1 in its shape. > > > > I agree with your last sentence -- row vectors and column vectors are both > > ways of expressing vectors using matrices. But that doesn't mean they > > don't exist. > > > > Given a vector v > > ,:v > > produces the corresponding row vector and > > ,.v > > produces the corresponding column vector. > > > > I think it's often simpler to just work with vectors, but a mathematician > > who wants to apply a proof about matrices to a vector might find > > row or column vectors more suitable. > > > > -- > > Raul > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
