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.

Key words and phrases. Matrix norm, power norm, \(p\)-norm, induction sets, induction curves, eigenvectors, \(p\)-eigenvectors.