document .inv.A

Author: perazz

doc/specs/stdlib_linalg.md

@@ -887,7 +887,7 @@ This interface is equivalent to the `pure` version of determinant [[stdlib_linal
 
 ### Return value
 
-Returns a real scalar value that represents the determinnt of the matrix.
+Returns a real scalar value that represents the determinant of the matrix.
 
 Raises `LINALG_ERROR` if the matrix is singular.
 Raises `LINALG_VALUE_ERROR` if the matrix is non-square.
@@ -898,3 +898,37 @@ Exceptions trigger an `error stop`.
 ```fortran
 {!example/linalg/example_determinant2.f90!}
 ```
+
+## `.inv.` - Inverse operator of a square matrix
+
+### Status
+
+Experimental
+
+### Description
+
+This operator returns the inverse of a `real` or `complex` square matrix \( A \).
+The inverse \( A^{-1} \) is defined such that \( A \cdot A^{-1} = A^{-1} \cdot A = I_n \).
+
+This interface is equivalent to the function version of  [[stdlib_linalg(module):inv(interface)]]. 
+
+### Syntax
+
+`b = ` [[stdlib_linalg(module):operator(.inv.)(interface)]] `(a)`
+
+### Arguments
+
+`a`: Shall be a rank-2 square array of any `real` or `complex` kinds. It is an `intent(in)` argument.
+
+### Return value
+
+Returns a rank-2 square array with the same type, kind and rank as `a`, that contains the inverse of `a`.
+
+If the matrix is singular or non-square, the operator returns zeros.
+
+### Example
+
+```fortran
+{!example/linalg/example_inverse1.f90!}
+```
+

src/stdlib_linalg.fypp

@@ -589,6 +589,22 @@ module stdlib_linalg
 
   ! Operator interface
   interface operator(.inv.)
+    !! version: experimental 
+    !!
+    !! Inverse operator of a square matrix
+    !! ([Specification](../page/specs/stdlib_linalg.html#inv-inverse-operator-of-a-square-matrix))
+    !!
+    !!### Summary
+    !! Operator interface for computing the inverse of a square `real` or `complex` matrix.
+    !!
+    !!### Description
+    !! 
+    !! This operator interface provides a convenient way to compute the inverse of a matrix.
+    !! Supported data types include `real` and `complex`.
+    !!
+    !!@note The provided functions are intended for square matrices.
+    !!@note BLAS/LAPACK backends do not currently support extended precision (``xdp``).
+    !!
     #:for rk,rt,ri in RC_KINDS_TYPES
     #:if rk!="xdp" 
     module function stdlib_linalg_inverse_${ri}$_operator(a) result(inva)