Matrix Inverse R←⌹Y

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