Add specification for computing the dot product (linalg: vecdot) (#137)

* Add dot product specification

* Update specification

* Fix output shape

* Update description

* Update copy

* Update copy

* Rename to inner_dot

* Update dtype requirements

* Rename to vecdot

Author: kgryte

spec/API_specification/linear_algebra_functions.md

@@ -115,11 +115,6 @@ Returns the specified diagonals. If `x` has more than two dimensions, then the a
 
     -   if `x` is a two-dimensional array, a one-dimensional array containing the diagonal; otherwise, a multi-dimensional array containing the diagonals and whose shape is determined by removing `axis1` and `axis2` and appending a dimension equal to the size of the resulting diagonals. The returned array must have the same data type as `x`.
 
-(function-dot)=
-### dot()
-
-TODO
-
 (function-eig)=
 ### eig()
 
@@ -400,3 +395,33 @@ Transposes (or permutes the axes (dimensions)) of an array `x`.
 -   **out**: _<array>_
 
     -   an array containing the transpose. The returned array must have the same data type as `x`.
+
+(function-vecdot)=
+### vecdot(x1, x2, /, *, axis=None)
+
+Computes the (vector) dot product of two arrays.
+
+#### Parameters
+
+-   **x1**: _<array>_
+
+    -   first input array. Should have a numeric data type.
+
+-   **x2**: _<array>_
+
+    -   second input array. Must be compatible with `x1` (see {ref}`broadcasting`). Should have a numeric data type.
+
+-   **axis**: _Optional\[ int ]_
+
+    -   axis over which to compute the dot product. Must be an integer on the interval `[-N, N)`, where `N` is the rank (number of dimensions) of the shape determined according to {ref}`broadcasting`. If specified as a negative integer, the function must determine the axis along which to compute the dot product by counting backward from the last dimension (where `-1` refers to the last dimension). If `None`, the function must compute the dot product over the last axis. Default: `None`.
+
+#### Returns
+
+-   **out**: _<array;>_
+
+    -   if `x1` and `x2` are both one-dimensional arrays, a zero-dimensional containing the dot product; otherwise, a non-zero-dimensional array containing the dot products and having rank `N-1`, where `N` is the rank (number of dimensions) of the shape determined according to {ref}`broadcasting`. The returned array must have a data type determined by {ref}`type-promotion`.
+
+#### Raises
+
+-   if provided an invalid `axis`.
+-   if the size of the axis over which to compute the dot product is not the same for both `x1` and `x2`.