# elementwise operation
create or replace function mm_op(TableA, op, TableB) as table (
  with TA as (from query_table(TableA)),
       TB as (from query_table(TableB)),
       tuple as
        (select TA.i as i, TA.j as j,
          ((select last(value) from TA where i=TB.i and j = TB.j),
           (select last(value) from TB where i=TA.i and j = TA.j)) as value
         from TA inner join TB
         on TA.i = TB.i and TA.j = TB.j)
  select i, j,
         case op when '+' then value[1] + value[2]
                 when '-' then value[1] - value[2]
                 when '*' then value[1] * value[2]
                 when '/' then value[1] / value[2]
                 when '^' then value[1] ^ value[2]
         else error('unknown op: ' || op)
         end as value
  from tuple
);

# scalar/matrix elementwise addition, preserving all columns
create or replace function sm_add(x, TableA) as table (
  select COLUMNS(* EXCLUDE(value)), (x + value) as value
  from query_table(TableA)
);

# scalar/matrix elementwise multiplication, preserving all columns
create or replace function sm_multiply(x, TableA) as table (
  select COLUMNS(* EXCLUDE(value)), (x * value) as value
  from query_table(TableA)
);

create or replace function matrix_elementwise_power(TableA, x) as table (
  select COLUMNS(* EXCLUDE(value)), (value ^ x) as value
  from query_table(TableA)
);

### Examples
create or replace table A (i integer, j integer, value float );
insert into A values
  (1, 1, 1),
  (1, 2, 2),
  (1, 3, 3),
  (2, 1, 2),
  (2, 2, 5),
  (2, 3, 7);

create or replace table B (i integer, j integer, value float );
insert into B values
  (1, 1, 2),
  (1, 2, 4),
  (1, 3, 8),
  (2, 1, 1),
  (2, 2, 5),
  (2, 3, 10);

from mm_op('A', '+', 'B');