Rayleigh Quotient

Problem

Compute the Rayleigh quotient of matrix A with respect to nonzero vector v:

R(A, v) = (v . (A*v)) / (v . v)

Return None if v is the zero vector.

Hint

For an eigenvector the Rayleigh quotient equals its eigenvalue.

case 1

in: [[[2,0],[0,3]],[1,0]]

expected: 2

case 2

in: [[[2,0],[0,3]],[1,1]]

expected: 2.5

case 3

in: [[[4,1],[2,3]],[1,1]]

expected: 5

case 4

in: [[[1,0],[0,1]],[0,0]]

expected: null

Starter codePython

def rayleigh_quotient(A, v):
    # Your code here
    pass

4 test cases · run your code against them in the editor