Find the eigenvalues of the matrix [[0, 1], [-1, 0]]

Published on December 1, 2024

Linear-Algebra

The eigenvalues of the matrix [[0, 1], [-1, 0]] are i and -i.

Question

eigenvalues of [[0, 1], [-1, 0]]

Answer

Here’s how to find the eigenvalues of the matrix

Find the characteristic equation. The characteristic equation is given by , where is the matrix, represents the eigenvalues, and is the identity matrix.

In our case, and . So, .

The determinant of this matrix is .

Therefore, the characteristic equation is .
Solve for . We have the equation . Subtracting 1 from both sides gives . Taking the square root of both sides gives .

So, the eigenvalues are

and

Final Answer: The final answer is

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