The V O
(calc-outer-product) [outer] command
applies a given binary operator to all possible pairs of elements
from two vectors, to produce a matrix. For example, V O
* with ‘[a,
b]’ and ‘[x,
y, z]’ on the stack produces a multiplication
table: ‘[[a x, a y, a z], [b x, b
y, b z]]’. Element r,c
of the result matrix is obtained by applying the operator to
element r of the lefthand vector and element
c of the righthand vector.
The V I
(calc-inner-product) [inner] command
computes the generalized inner product of two vectors or
matrices, given a “multiplicative” operator and an
“additive” operator. These can each actually be any
binary operators; if they are ‘*’ and ‘+’, respectively, the result is a
standard matrix multiplication. Element r,c
of the result matrix is obtained by mapping the multiplicative
operator across row r of the lefthand matrix and
column c of the righthand matrix, and then reducing
with the additive operator. Just as for the standard *
command, this can also do a vector-matrix or matrix-vector inner
product, or a vector-vector generalized dot product.
Since V I requires two operators, it prompts twice. In each case, you can use any of the usual methods for entering the operator. If you use $ twice to take both operator formulas from the stack, the first (multiplicative) operator is taken from the top of the stack and the second (additive) operator is taken from second-to-top.