DETERMINANT (2) The phrases ΓÇô/ . * and +/ . * are the determinant and permanent of square matrix arguments. More generally, u . v is defined in terms of a recursive expansion by minors:
('$.=. 1+1=#y.';b;'y.') : '' where b is:
'(0{|:y.)u . v $:"2 (<&.>&.>{0;~i.#y.){y.'
DOT PRODUCT (_ _) For vectors and matrices, x+/ . *y is equivalent to the dot, inner, or matrix product of math, and other rank-0 verbs such as <. and *. are treated analogously: If r=. lv,lv>.<:$$y and ip=. u@(v"r"(>:lv,_)) then x ip y is x u . v y.
In other words, u is applied to each of the items produced by applying v to each item of the list of "left-argument cells", and the items of y. The shapes of x and y must be such that the number of items in these left and right arguments agree. For example, if v has ranks 2 and 3, the shape of the result is sr, and the shapes of x and y are 2 3 4 5 6 and 4 7 8 9 10 11, then the overall shape is 2 3 7 8,sr.
