50.2 MatScalarProducts

MatScalarProducts( tbl, chars1, chars2 )
MatScalarProducts( tbl, chars )

For a character table tbl and two lists chars1, chars2 of characters, the first version returns the matrix of scalar products (see ScalarProduct); we have

'MatScalarProducts( <tbl>, <chars1>, <chars2> )[i][j]' = 'ScalarProduct( <tbl>, <chars1>[j], <chars2>[i] )',

i.e., row i contains the scalar products of chars2[i] with all characters in chars1.

The second form returns a lower triangular matrix of scalar products:

'MatScalarProducts( <tbl>, <chars> )[i][j]' = 'ScalarProduct( <tbl>, <chars>[j], <chars>[i] )'

for 'j' leq 'i'.

    gap> t:= CharTable( "A5" );;
    gap> chars:= Sublist( t.irreducibles, [ 2 .. 4 ] );;
    gap> chars:= Set( Tensored( chars, chars ) );;
    gap> MatScalarProducts( t, chars );
    [ [ 2 ], [ 1, 3 ], [ 1, 2, 3 ], [ 2, 2, 1, 3 ], [ 2, 1, 2, 2, 3 ],
      [ 2, 3, 3, 3, 3, 5 ] ]

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