An index formula for the product of linear relations
A Sandovici, H de Snoo - Linear algebra and its applications, 2009 - Elsevier
A Sandovici, H de Snoo
Linear algebra and its applications, 2009•Elsevier… The main result of this note is a formula which relates the nullities and the defects of the
relations A and B with those of the product relation BA. © 2009 Elsevier Inc. All rights
reserved. … A linear relation, or relation for short, A from the linear space X to the linear
space Y is a (linear) subspace of the space X × Y, the Cartesian product of X with Y. Denote
by L(X, Y) the class of all linear relations from the linear space X to the linear space Y. The
notations dom A and ran A denote the domain and the range of A, which are the …
relations A and B with those of the product relation BA. © 2009 Elsevier Inc. All rights
reserved. … A linear relation, or relation for short, A from the linear space X to the linear
space Y is a (linear) subspace of the space X × Y, the Cartesian product of X with Y. Denote
by L(X, Y) the class of all linear relations from the linear space X to the linear space Y. The
notations dom A and ran A denote the domain and the range of A, which are the …
Let X,Y, and Z be linear spaces and let A and B be linear relations from X to Y and from Y to Z, respectively. The main result of this note is a formula which relates the nullities and the defects of the relations A and B with those of the product relation BA.
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