Worksheet: The Rayleigh Principle for Finding Eigenvalues

Practice

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 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 3 √ 2
  • E 1 4 √ 3

Q2:

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

  • A10
  • B7
  • C √ 3
  • D √ 6
  • E √ 5

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