26.16. Dual Spaces

Try these first

1. 1.

   Define a dual space in your own words.

   Hint

   Think about what functionals do with vectors.

2. 2.

   What is a linear functional?

   Hint

   Look for definitions in your notes.

3. 3.

   What is the relationship between the dual space and the original vector space's dimension?

   • Same dimension
   • Half of the dimension
   • Double the dimension

   Hint

   Think about the definition of duality.

4. 4.

   A linear functional maps vectors to numbers. True or False?

   • True
   • False

   Hint

   Reflect on the meaning of functionals.

5. 5.

   Define linear functionals for specific vector spaces of dimensions 3 and 4, and demonstrate how they relate via duality.

   Hint

   Check if adding vectors and scaling works.

6. 6.

   Illustrate the usage of dual spaces in virtual work within a mechanical system.

   Hint

   Consider the role of energies in virtual work principles.