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Price, Geoffrey L.
Linear algebra and its applications, 06/2022, Letnik: 642Journal Article
Let (a)=a0,a1,a2,… be a sequence over any finite field F with a0=0. For each positive integer n, let An be the associated n×n skew-symmetric Toeplitz matrixa0a1a2a3⋯an−1−a1a0a1a2⋯an−2−a2−a1a0a1⋯an−3⋮⋮⋮⋮⋱⋮−an−1−an−2−an−3……a0. If the sequence is eventually periodic but not mirror periodic, then the nullity sequence {νn=null(An):n∈N} is also eventually periodic, where νn=null(An) is the nullity of the matrix An. For s a certain multiple of the period of the nullity sequence, a recursion formula produces the vectors in ker(An+qs) from those in ker(An), for n sufficiently large and for non-negative integers q.
