On the construction of \(p\)-eigenvectors

Abstract. Recent investigations led to the definition of \(p\)-eigenvectors: such vectors for a matrix, that the fraction of the vector norms of the matrix-vector product and the nonzero vector (as in defining a natural matrix norm) is independent of the applied \(p\)-norm. This paper elaborates this concept further, presenting general results, proof of existence for arbitrary matrices, and constructing new solutions in the case of \(3 \times 3\) diagonal matrices.