26.12. Inner Product Spaces

Try these first

1. 1.

   Define an inner product space.

   Hint

   Think about the properties that define how vectors interact.

2. 2.

   What does orthogonal mean?

   Hint

   This is related to angles between vectors.

3. 3.

   What is an inner product space?

   • A structure without parameters
   • A vector space with an inner product
   • A space with no defined operations

   Hint

   Think about the components of an inner product.

4. 4.

   True or False: The inner product of two orthogonal vectors is always zero.

   • True
   • False

   Hint

   Consider what orthogonal means.

5. 5.

   Given vectors A = (1, 2, 3) and B = (4, -1, 2), calculate their inner product and determine if they are orthogonal.

   Hint

   Remember the definition of the inner product.

6. 6.

   For vectors X = (0, 0) and Y = (2, 3), confirm if they are orthogonal using the inner product.

   Hint

   Evaluate the vector components directly.