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basis. To transform to the eigenvector basis we’ve multiplied by 𝑄⊺; So to transform back from the eigenvector basis we multiply by the inverse of 𝑄⊺ which is 𝑄. 𝑦⃗ = 𝑄⊺𝑥⃗ ⟹ 𝑥⃗ = 𝑄𝑦⃗ The eigenvectors of 𝐴 are [-1/√2, 1/√2] and [1/√2, 1/√2] in their normalized form. So the eigenvector matrix 𝑄 is: