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Pascal eigenspaces and invariant sequences of the first or second kind

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Abstract An infinite real sequence { a n } is called an invariant sequence of the first (resp., second) kind if a n = ∑ k = 0 n (… Click to show full abstract

Abstract An infinite real sequence { a n } is called an invariant sequence of the first (resp., second) kind if a n = ∑ k = 0 n ( n k ) ( − 1 ) k a k (resp., a n = ∑ k = n ∞ ( k n ) ( − 1 ) k a k ). We review and investigate invariant sequences of the first and second kind, and study their relationships using similarities of Pascal-type matrices and their eigenspaces.

Keywords: second kind; sequences first; kind; first second; pascal eigenspaces; invariant sequences

Journal Title: Linear Algebra and its Applications
Year Published: 2017

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