Question

Let us consider a 3×3 matrix A with Eigen values of λ1, λ2, λ3 and the Eigen values of A^-1 are?

(a) λ1, λ2, λ3

(b) \( \frac{1}{λ_1}, \frac{1}{λ_2}, \frac{1}{λ_3}\)

(c) -λ1, -λ2, -λ3

(d) λ1, 0, 0

This question was posed to me in a dream while sleeping

I need to ask this question from Eigenvalues topic in section Linear Algebra Overview of Signals and Systems

Answer 1

Right choice is (b) \( \frac{1}{λ_1}, \frac{1}{λ_2}, \frac{1}{λ_3}\)

To explain I would say: According to the property of the Eigen values, if  is the Eigen value of A, then \( \frac{1}{λ}\) is the Eigen value of A^-1.

So the Eigen values of A^-1 are \( \frac{1}{λ_1}, \frac{1}{λ_2}, \frac{1}{λ_3}\).