Linear preservers of parallel matrix pairs with respect to the k-numerical radius

Let 1 ≤ k < n be integers. Two n × n matrices A and B form a parallel pair with respect to the k-numerical radius wₖ if wₖ(A + μ B) = wₖ(A) + wₖ(B) for some scalar μ with |μ| = 1; they form a TEA (triangle equality attaining) pair if the preceding equation holds for μ = 1. We classify linear bijections on Mₙ and on Hₙ which preserve parallel pairs or TEA pairs. Such preservers are scalar multiples of wₖ-isometries, except for some exceptional maps on Hₙ when $n=2k$.