Dimensional formula

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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



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, .