BUG: Fix typecasting problem in scipy.sparse.lil_matrix truediv (#19408)

* Fix typecasting problem in lil_matrix truedriv

* Added test

---------

Co-authored-by: Dan Schult <dschult@colgate.edu>

scipy/sparse/_lil.py

@@ -287,6 +287,7 @@ def _mul_scalar(self, other):
     def __truediv__(self, other):           # self / other
         if isscalarlike(other):
             new = self.copy()
+            new.dtype = np.result_type(self, other)
             # Divide every element by this scalar
             for j, rowvals in enumerate(new.data):
                 new.data[j] = [val/other for val in rowvals]

scipy/sparse/tests/test_base.py

@@ -4201,6 +4201,14 @@ def test_scalar_mul(self):
         x = x*0
         assert_equal(x[0, 0], 0)
 
+    def test_truediv_scalar(self):
+        A = self.spcreator((3, 2))
+        A[0, 1] = -10
+        A[2, 0] = 20
+
+        assert_array_equal((A / 1j).toarray(), A.toarray() / 1j)
+        assert_array_equal((A / 9).toarray(), A.toarray() / 9)
+
     def test_inplace_ops(self):
         A = lil_matrix([[0, 2, 3], [4, 0, 6]])
         B = lil_matrix([[0, 1, 0], [0, 2, 3]])