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

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

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

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