Find the Eigenvalues [[0,1],[-1,0]]

Problem

[[0,1],[−1,0]]

Solution

1. Set up the characteristic equation by finding the determinant of A−λ*I where I is the identity matrix and λ represents the eigenvalues.

det(0−λ)=0

2. Calculate the determinant of the 2×2 matrix by applying the formula a*d−b*c

(−λ)*(−λ)−(1)*(−1)=0

3. Simplify the expression to obtain the characteristic polynomial.

λ2+1=0

4. Solve for λ by isolating the variable and taking the square root of both sides.

λ2=−1

5. Identify the complex roots since the square root of a negative number involves the imaginary unit i

λ=±i

Final Answer

λ=i,−i

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