V.—A Development of a Pfaffian having a Vacant Minor

Extract

(1) The simplest possible case of the development referred to in the title is one which is seen to follow instantly from the determinant definition of a Pfaffian. Thus, by the said definition,

and therefore

the result reached being that a Pfaffian with certain zero elements is expressible as a determinant. It should be noted that, as in many instances where this form of definition is used, there is an ambiguity as to sign : it is of less importance to note that here the appropriate sign is –.