GATE 2023 Electronics & Communication Q15

Question

Let the sets of eigenvalues and eigenvectors of a matrix B be {λk | 1 ≤ k ≤ n} and {vk | 1 ≤ k ≤ n}, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where B = P⁻¹AP, respectively, are

Answer

{λk det(A) | 1 ≤ k ≤ n} and {Pvk | 1 ≤ k ≤ n}

Answer

{λk | 1 ≤ k ≤ n} and {vk | 1 ≤ k ≤ n}

Answer

{λk | 1 ≤ k ≤ n} and {Pvk | 1 ≤ k ≤ n}

Answer

{λk | 1 ≤ k ≤ n} and {P⁻¹vk | 1 ≤ k ≤ n}