diff --git a/doc/specs/stdlib_linalg.md b/doc/specs/stdlib_linalg.md
index cab16279c..7ca3b9198 100644
--- a/doc/specs/stdlib_linalg.md
+++ b/doc/specs/stdlib_linalg.md
@@ -101,21 +101,41 @@ end program demo_diag5
 
 Experimental
 
+### Class
+
+Pure function.
+
 ### Description
 
-Construct the identity matrix
+Construct the identity matrix.
 
 ### Syntax
 
-`I = [[stdlib_linalg(module):eye(function)]](n)`
+`I = [[stdlib_linalg(module):eye(function)]](dim1 [, dim2])`
 
 ### Arguments
 
-`n`: Shall be a scalar of default type `integer`. 
+`dim1`: Shall be a scalar of default type `integer`.
+This is an `intent(in)` argument. 
+
+`dim2`: Shall be a scalar of default type `integer`.
+This is an `intent(in)` and `optional` argument. 
 
 ### Return value
 
-Returns the identity matrix, i.e. a square matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer(int8)`.
+Return the identity matrix, i.e. a matrix with ones on the main diagonal and zeros elsewhere. The return value is of type `integer(int8)`.
+The use of `int8` was suggested to save storage.
+
+#### Warning
+
+Since the result of `eye` is of `integer(int8)` type, one should be careful about using it in arithmetic expressions. For example:
+```fortran
+real :: A(:,:)
+!> Be careful
+A = eye(2,2)/2     !! A == 0.0
+!> Recommend
+A = eye(2,2)/2.0   !! A == diag([0.5, 0.5])
+```
 
 ### Example
 
@@ -123,8 +143,16 @@ Returns the identity matrix, i.e. a square matrix with ones on the main diagonal
 program demo_eye1
     use stdlib_linalg, only: eye
     implicit none
+    integer :: i(2,2)
     real :: a(3,3)
-    A = eye(3)
+    real :: b(2,3)  !! Matrix is non-square.
+    complex :: c(2,2)
+    I = eye(2)              !! [1,0; 0,1]
+    A = eye(3)              !! [1.0,0.0,0.0; 0.0,1.0,0.0; 0.0,0.0,1.0]
+    A = eye(3,3)            !! [1.0,0.0,0.0; 0.0,1.0,0.0; 0.0,0.0,1.0]
+    B = eye(2,3)            !! [1.0,0.0,0.0; 0.0,1.0,0.0]
+    C = eye(2,2)            !! [(1.0,0.0),(0.0,0.0); (0.0,0.0),(1.0,0.0)]
+    C = (1.0,1.0)*eye(2,2)  !! [(1.0,1.0),(0.0,0.0); (0.0,0.0),(1.0,1.0)]
 end program demo_eye1
 ```
 
diff --git a/src/stdlib_linalg.fypp b/src/stdlib_linalg.fypp
index 5e0388c0b..3faaeb9af 100644
--- a/src/stdlib_linalg.fypp
+++ b/src/stdlib_linalg.fypp
@@ -5,6 +5,7 @@ module stdlib_linalg
   !! ([Specification](../page/specs/stdlib_linalg.html))
   use stdlib_kinds, only: sp, dp, qp, &
     int8, int16, int32, int64
+  use stdlib_optval, only: optval
   implicit none
   private
 
@@ -82,20 +83,28 @@ module stdlib_linalg
 
 contains
 
-    function eye(n) result(res)
-      !! version: experimental
-      !!
-      !! Constructs the identity matrix
-      !! ([Specification](../page/specs/stdlib_linalg.html#description_1))
-      integer, intent(in) :: n
-      integer(int8) :: res(n, n)
-      integer :: i
-      res = 0
-      do i = 1, n
-         res(i, i) = 1
-      end do
-    end function eye
+    !> Version: experimental
+    !>
+    !> Constructs the identity matrix.
+    !> ([Specification](../page/specs/stdlib_linalg.html#eye-construct-the-identity-matrix))
+    pure function eye(dim1, dim2) result(result)
+
+        integer, intent(in) :: dim1
+        integer, intent(in), optional :: dim2
+        integer(int8), allocatable :: result(:, :)
+
+        integer :: dim2_
+        integer :: i
 
+        dim2_ = optval(dim2, dim1)
+        allocate(result(dim1, dim2_))
+        
+        result = 0_int8
+        do i = 1, min(dim1, dim2_)
+            result(i, i) = 1_int8
+        end do
+
+    end function eye
 
     #:for k1, t1 in RCI_KINDS_TYPES
       function trace_${t1[0]}$${k1}$(A) result(res)
@@ -108,4 +117,5 @@ contains
         end do
       end function trace_${t1[0]}$${k1}$
     #:endfor
-end module
+
+end module stdlib_linalg
diff --git a/src/tests/Makefile.manual b/src/tests/Makefile.manual
index 7ab184016..c29170e24 100644
--- a/src/tests/Makefile.manual
+++ b/src/tests/Makefile.manual
@@ -11,3 +11,4 @@ all test clean:
 	$(MAKE) -f Makefile.manual --directory=stats $@
 	$(MAKE) -f Makefile.manual --directory=string $@
 	$(MAKE) -f Makefile.manual --directory=math $@
+	$(MAKE) -f Makefile.manual --directory=linalg $@
diff --git a/src/tests/linalg/Makefile.manual b/src/tests/linalg/Makefile.manual
new file mode 100644
index 000000000..a95f600c7
--- /dev/null
+++ b/src/tests/linalg/Makefile.manual
@@ -0,0 +1,4 @@
+PROGS_SRC = test_linalg.f90
+
+
+include ../Makefile.manual.test.mk
diff --git a/src/tests/linalg/test_linalg.f90 b/src/tests/linalg/test_linalg.f90
index cc8d0db68..7583f0585 100644
--- a/src/tests/linalg/test_linalg.f90
+++ b/src/tests/linalg/test_linalg.f90
@@ -81,12 +81,19 @@ subroutine test_eye
     integer :: i
     write(*,*) "test_eye"
 
+    call check(all(eye(3,3) == diag([(1,i=1,3)])), &
+               msg="all(eye(3,3) == diag([(1,i=1,3)])) failed.",warn=warn)
+    
+    rye = eye(3,4)
+    call check(sum(abs(rye(:,1:3) - diag([(1.0_sp,i=1,3)]))) < sptol, &
+          msg="sum(abs(rye(:,1:3) - diag([(1.0_sp,i=1,3)]))) < sptol failed", warn=warn)
+
     call check(all(eye(5) == diag([(1,i=1,5)])), &
           msg="all(eye(5) == diag([(1,i=1,5)] failed.",warn=warn)
     
     rye = eye(6)
-    call check(sum(rye - diag([(1.0_sp,i=1,6)])) < sptol, &
-          msg="sum(rye - diag([(1.0_sp,i=1,6)])) < sptol failed.",warn=warn)
+    call check(sum(abs(rye - diag([(1.0_sp,i=1,6)]))) < sptol, &
+          msg="sum(abs(rye - diag([(1.0_sp,i=1,6)]))) < sptol failed.",warn=warn)
 
     cye = eye(7)
     call check(abs(trace(cye) - cmplx(7.0_sp,0.0_sp,kind=sp)) < sptol, &