TR3.5

Operators (linear algebra)

Exr0n 2021-09-27 Mon 11:51

1 Operator, \(\mathcal L(V)\)   def

  • A linear map from a vector space \(V\) to itself is called an operator.
  • The notation \(\mathcal L(V)\) means \(\mathcal L(V, V)\) which is the set of all operators on \(V\).

1.1 results

1.1.1 Axler3.69 Injectivity is surjectivity in finite dimensions

In a finite dimension operator, invertability, injectivity, and surjectivity are equivalent.