Dimensional formula
The dimensional formula comes from the mathematical branch of linear algebra . It indicates how the dimension of the sum of two finite-dimensional sub-vector spaces , a larger vector space, can be calculated:
It follows directly from the ranking . The situation is a special case (see direct sum ). In this case the dimensional formula is reduced to
since applies to a direct sum
The sub-vector space represented by the intersection of and is thus the zero vector space , the dimension of which is equal to zero.
If or is infinite dimensional, it is no longer possible to carry out the subtraction . However, it applies in any case
and
- .
Since for two cardinal numbers , of which at least one endless , the sum is equal to the maximum of the two, that is, in the case that one of the two partial spaces is infinite dimensional, .
literature
- Siegfried Bosch : Linear Algebra. Springer-Verlag, 2001, ISBN 3-540-41853-9 , pp. 46-47.