Y must be a simple array of rank 2 or less. Y must be non-singular. If Y is a scalar, it is treated as a one-element matrix. If Y is a vector, it is treated as a single-column matrix. Y must have at least the same number of rows as columns.
R is the inverse of Y if Y is a square matrix, or the left inverse of Y if Y is not a square matrix. That is, R+.×Y is an identity matrix.
The shape of R is ⌽⍴Y.
Examples
M 2 ¯3 4 10 +A←⌹M 0.3125 0.09375 ¯0.125 0.0625
Within calculation accuracy, A+.×M is the identity matrix.
A+.×M
1 0
0 1
j←{⍺←0 ⋄ ⍺+0J1×⍵}
x←j⌿¯50+?2 5 5⍴100
x
¯37J¯41 25J015 ¯5J¯09 3J020 ¯29J041
¯46J026 17J¯24 17J¯46 43J023 ¯12J¯18
1J013 33J025 ¯47J049 ¯45J¯14 2J¯26
17J048 ¯50J022 ¯12J025 ¯44J015 ¯9J¯43
18J013 8J038 43J¯23 34J¯07 2J026
⍴x
5 5
id←{∘.=⍨⍳⍵} ⍝ identity matrix of order ⍵
⌈/,| (id 1↑⍴x) - x+.×⌹x
3.66384E¯16