29.1.1. Eigenvalues and Eigenvectors

Try these first

1. 1.

   Define eigenvalue.

   Hint

   Think about the equation involving a matrix and a vector.

2. 2.

   What is an eigenvector?

   Hint

   Focus on the relationship between the vector and the matrix.

3. 3.

   What is the eigenvalue of a matrix?

   • A moment of a vector
   • A measure of structure's stiffness
   • A scalar associated with a matrix transformation

   Hint

   Focus on the transformation equation.

4. 4.

   True or False: An eigenvector can be the zero vector.

   • True
   • False

   Hint

   Think about the definition of eigenvectors.

5. 5.

   Given matrix A = [[4, 2], [1, 3]], compute the eigenvalues and eigenvectors.

   Hint

   Don't forget to substitute each λ back to find eigenvectors.

6. 6.

   Discuss the implications of geometric multiplicity in real-world structures.

   Hint

   Link it to how stresses distribute in materials.