SELECT '[1,2,3]'::vector + '[4,5,6]';
 ?column? 
----------
 [5,7,9]
(1 row)

SELECT '[1,2,3]'::vector - '[4,5,6]';
  ?column?  
------------
 [-3,-3,-3]
(1 row)

SELECT vector_dims('[1,2,3]');
 vector_dims 
-------------
           3
(1 row)

SELECT round(vector_norm('[1,1]')::numeric, 5);
  round  
---------
 1.41421
(1 row)

SELECT vector_norm('[3,4]');
 vector_norm 
-------------
           5
(1 row)

SELECT vector_norm('[0,1]');
 vector_norm 
-------------
           1
(1 row)

SELECT l2_distance('[0,0]', '[3,4]');
 l2_distance 
-------------
           5
(1 row)

SELECT l2_distance('[0,0]', '[0,1]');
 l2_distance 
-------------
           1
(1 row)

SELECT l2_distance('[1,2]', '[3]');
ERROR:  different vector dimensions 2 and 1
SELECT inner_product('[1,2]', '[3,4]');
 inner_product 
---------------
            11
(1 row)

SELECT inner_product('[1,2]', '[3]');
ERROR:  different vector dimensions 2 and 1
SELECT cosine_distance('[1,2]', '[2,4]');
 cosine_distance 
-----------------
               0
(1 row)

SELECT cosine_distance('[1,2]', '[0,0]');
 cosine_distance 
-----------------
             NaN
(1 row)

SELECT cosine_distance('[1,1]', '[1,1]');
 cosine_distance 
-----------------
               0
(1 row)

SELECT cosine_distance('[1,1]', '[-1,-1]');
 cosine_distance 
-----------------
               2
(1 row)

SELECT cosine_distance('[1,2]', '[3]');
ERROR:  different vector dimensions 2 and 1
SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
    avg    
-----------
 [2,3.5,5]
(1 row)

SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
    avg    
-----------
 [2,3.5,5]
(1 row)

SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
 avg 
-----
 
(1 row)

SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
ERROR:  expected 2 dimensions, not 1
SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
ERROR:  vector cannot have more than 16000 dimensions