On 8/9/06, Roger Hui <[EMAIL PROTECTED]> wrote:
> Now, with respect to J, the interesting fact is that,
> although A,B,:C is of shape 3 2, the expression
> det A,B,:C
> correctly computes the same oriented area of ABC.
> I discovered for myself this behaviour of J several
> years ago. To my knowledge, it is not documented.
> Apparently J computes `determinants' of matrices of
> any shape. At least it does not object to. :)
The dictionary entry says:
http://www.jsoftware.com/books/help/dictionary/d300.htm
The phrases -/ . * and +/ . * are the determinant
and permanent of square matrix arguments. More
generally, the phrase u . v is defined in terms of
a recursive expansion by minors along the first
column, as discussed below.
And two of the examples that follow are not on
square matrices. Given that, it would take a perverse interpretation to
conclude that the monad
u . v does NOT work on non-square matrices.
Sorry, I really haven't read the examples so far, and
groking the definition of u . v as written in J is beyond
my abilities.
As for the text from the dictionary, I concluded that the
said generalization is only w.r.t. u and v.
I do not believe it suggests generalizing towards non-square
matrices, as it speaks of `minors', and the only minors I
know of are determinants (i.e., pertain to square matrices).
Note that I did NOT say that ``the monad u . v does NOT
work on non-square matrices''. What I said was that the fact
of producing a `determinant' in the particular way which I
described, to my knowledge, was not documented (unless
one undestands enough J to read the definition of u . v in J).
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