Worksheet: The Rayleigh Principle for Finding Eigenvalues

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
  • B223
  • C√2
  • D14√3
  • E13√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

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