Week4 Quiz 9 proving

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
1

Deer, Deeplearning.AI
I want to know how to prove quiz 9 statement (1/i is an eigenvalue of inverse matrix of A) is right.
Please let me know

2

Hi @rlaskan95

It was mentioned in the lecture that the eigenvalues of the inverse matrix are equal to the inverse of the eigenvalues of the original matrix

For proving, think of any matrix with an eigenvalue = i.

For example, matrix A
[i, 0]
[0,1]
has one of its eigenvalues equal to i

The matrix inverse A^{-1}
[1/i, 0]
[0, 1]
has one of its eigenvalues equal to 1/i

Note that

1/i = -i

To convert from one form to another, simply multiply both sides with

i/i

3

@jonrico am still unable to understand how to solve this question, could you please help to explain it step by step - thanks

4

Hi @vakulgoyle.

The first sentence can already solve the question.
Please be specific where you are having difficulty.

Which of these steps are unfamiliar to you?

  • Calculating eigenvalues
  • Calculating inverse matrix
  • Working with imaginary number i
5

Hey @jonrico I figured it out on how to solve this - thanks :slight_smile: