Note: the present entry employs the terminology and notation defined and described in the entry on tensor arrays. To keep things reasonably self contained we mention that the symbol refers to the vector space of type tensor arrays, i.e. maps
where is some finite list of index labels, and where is a field.
that combines a type tensor array and a type tensor array to produce a type tensor array (also written as ), defined by
Speaking informally, what is going on above is that we multiply every value of the array by every possible value of the array, to create a new array, . Quite obviously then, the size of is the size of times the size of , and the index slots of the product are just the union of the index slots of and of .
and thereby endow the latter with the structure of an -algebra11We will not pursue this line of thought here, because the topic of algebra structure is best dealt with in the a more abstract context. The same comment applies to the use of the tensor product sign in denoting outer multiplication. These topics are dealt with in the entry pertaining to abstract tensor algebra..
|Date of creation||2013-03-22 12:40:31|
|Last modified on||2013-03-22 12:40:31|
|Last modified by||rmilson (146)|