Class 5
Two Special Subspaces
-
Range and Nullspace of a Linear
Transformation T - connected to the properties of
onto and one-one, respectively, Section 4.1;
(video presentation - click on lecture #10)
-
Definitions, examples and properties:
-
rank is dim of range space and
- nullity is dim of nullspace (kernel).
- Both the range space and nullspace are subspaces
- The nullity of T is 0 iff T is one-one.
(Note: By assigning a dimension to a vector space, we have implicitly
assumed that the vector space is finite dimensional.)