DOC: vdot: adjustments per review

Author: mdhaber

numpy/_core/multiarray.py

@@ -842,20 +842,22 @@ def dot(a, b, out=None):
 
 @array_function_from_c_func_and_dispatcher(_multiarray_umath.vdot)
 def vdot(a, b):
-    """
+    r"""
     vdot(a, b, /)
 
     Return the dot product of two vectors.
 
-    The vdot(`a`, `b`) function handles complex numbers differently than
-    dot(`a`, `b`).  If the first argument is complex the complex conjugate
-    of the first argument is used for the calculation of the dot product.
+    The `vdot` function handles complex numbers differently than `dot`:
+    if the first argument is complex, it is replaced by its complex conjugate
+    in the dot product calculation. `vdot` also handles multidimensional
+    arrays differently than `dot`: it does not perform a matrix product, but
+    flattens the arguments to 1-D arrays before taking a vector dot product.
 
-    Note that `vdot` handles multidimensional arrays differently than `dot`: 
-    it does not perform a matrix product, but flattens input arguments to 1-D vectors first. 
-    The runtime of this function is linear in `a.size` and `b.size`. When `(a, b)` are 2-D arrays 
-    of the same shape, this function returns their `Frobenius inner-product` (also known as the 
-    *trace inner product* or the *standard inner product* on a vector space of matrices).
+    Consequently, when the arguments are 2-D arrays of the same shape, this
+    function effectively returns their
+    `Frobenius inner product <https://en.wikipedia.org/wiki/Frobenius_inner_product>`_.
+    (also known as the *trace inner product* or the *standard inner product*
+    on a vector space of matrices).
 
     Parameters
     ----------
@@ -896,7 +898,7 @@ def vdot(a, b):
     >>> 1*4 + 4*1 + 5*2 + 6*2
     30
 
-    """
+    """  # noqa: E501
     return (a, b)