Matrices, Eigenvalues, and the Size of a Linear Transformation
May 20, 2004
Bailey Hall 106
The study of linear transformations is one of the principal topics of linear algebra. Any student of the subject remembers, for example, that a linear transformation from Rn to Rn can be represented by an n × n matrix. This talk introduces the concept of the size (or more properly, the norm) of a linear transformation. We will discuss this concept in the context of finite-dimensional vector spaces, providing several concrete examples. We will also consider the topic in relation to certain linear transformations on infinite-dimensional vector spaces. As a final treat, we will state a few recent results along these lines, theorems proved by the speaker and by Professor Carswell.
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