Worksheet: The Rayleigh Principle for Finding Eigenvalues

Download

In this worksheet, we will practice finding an upper bound for the difference between the Rayleigh quotient principle and an eigenvalue of a matrix.

Q1:

Consider the matrix 𝐴=323214340, and the vector (1,1,1). Find an upper bound for the difference between the Rayleigh quotient and an eigenvalue of 𝐴.

  • A √ 3
  • B 2 2 3
  • C √ 2
  • D 1 4 √ 3
  • E 1 3 √ 2

Q2:

Consider the matrix 𝐴=121214145, and the vector (1,1,1). Find an upper bound for the difference between the Rayleigh quotient and an eigenvalue of 𝐴.

  • A √ 5
  • B √ 6
  • C √ 3
  • D10
  • E7

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.