On Fri, Jun 5, 2009 at 11:30 AM, Alan G Isaac <ais...@american.edu> wrote:
> On 6/5/2009 11:38 AM Olivier Verdier apparently wrote: > > I think matrices can be pretty tricky when used for > > teaching. For instance, you have to explain that all the > > operators work component-wise, except the multiplication! > > Another caveat is that since matrices are always 2x2, the > > "scalar product" of two column vectors computed as " x.T > > * y" will not be a scalar, but a 2x2 matrix. There is also > > the fact that you must cast all your vectors to column/raw > > matrices (as in matlab). For all these reasons, I prefer > > to use arrays and dot for teaching, and I have never had > > any complaints. > > > I do not understand this "argument". > You should take it very seriously when someone > reports to you that the matrix object is a crucial to them, > e.g., as a teaching tool. Even if you do not find > personally persuasive an example like > http://mail.scipy.org/pipermail/numpy-discussion/2009-June/043001.html > I have told you: this is important for my students. > Reporting that your students do not complain about using > arrays instead of matrices does not change this one bit. > > Student backgrounds differ by domain of application. In > economics, matrices are in *very* wide use, and > multidimensional arrays get almost no use. Textbooks in > econometrics (a huge and important field, even outside of > economics) are full of proofs using matrix algebra. > A close match to what the students see is crucial. > When working with multiplication or exponentiation, > matrices do what they expect, and 2d arrays do not. > > One more point. As Python users we get used to installing > a package here and a package there to add functionality. > But this is not how most people looking for a matrix > language see the world. Removing the matrix object from > NumPy will raise the barrier to adoption by social > scientists, and there should be a strongly persuasive reason > before taking such a step. > > Separately from all that, does anyone doubt that there is > code that depends on the matrix object? The core objection > to a past proposal for useful change was that it could break > extant code. I would hope that nobody who took that > position would subsequently propose removing the matrix > object altogether. > > Cheers, > Alan Isaac > > PS If x and y are "column vectors" (i.e., matrices), then > x.T * y *should* be a 1×1 matrix. > Since the * operator is doing matrix multiplication, > this is the correct result, not an anomaly. > Well, one could argue that. The x.T is a member of the dual, hence maps vectors to the reals. Usually the reals aren't represented by 1x1 matrices. Just my [.02] cents. Chuck
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