31.5. Canonical Forms (Brief Introduction)

Try these first

1. 1.

   What is Jordan Canonical Form?

   Hint

   Think about how matrices can be rearranged for simplicity.

2. 2.

   What constitutes a Jordan Block?

   Hint

   Consider the structure you see in those blocks.

3. 3.

   What does JCF stand for?

   • Jordan Canonical Form
   • Joint Coordinate Frame
   • Just Canonical Form

   Hint

   Think about the key terms in matrix theory.

4. 4.

   True or False: Every matrix can be diagonalized.

   • True
   • False

   Hint

   Recall the properties of eigenvalues.

5. 5.

   Given the matrix A = [[6, 1], [0, 6]], find its Jordan Canonical Form.

   Hint

   Look for the structure with repeated eigenvalues.

6. 6.

   Construct the JCF for a matrix that has a 3x3 block with an eigenvalue of 5 and two independent eigenvalues of 2.

   Hint

   Identify how to organize duplicate eigenvalues into blocks.