]]in [ ]arr[ out[ ]array( in [ ]arr arr[ out[ ]array([ ] ] ]] ]this is referred to as broadcasting and is explained in more detail in operations between dataframe and series are similarin [ ]frame dataframe(np arange( reshape(( ))columns=list('bde')index=['utah''ohio''texas''oregon']in [ ]series frame ix[ in [ ]frame out[ ] utah ohio texas oregon in [ ]series out[ ] nameutah by defaultarithmetic between dataframe and series matches the index of the series on the dataframe' columnsbroadcasting down the rowsin [ ]frame series out[ ] utah ohio texas oregon if an index value is not found in either the dataframe' columns or the series' indexthe objects will be reindexed to form the unionin [ ]series series(range( )index=[' '' '' ']in [ ]frame series out[ ] utah nan nan ohio nan nan texas nan nan oregon nan nan if you want to instead broadcast over the columnsmatching on the rowsyou have to use one of the arithmetic methods for examplein [ ]series frame[' 'in [ ]frame in [ ]series essential functionality www it-ebooks info