In many applications, we come across difference equations; the simplest of them is a first order vwxtor recurrence
\[ {\bf x}_{k+1} = {\bf A}\, {\bf x}+k , \qquad k=0,1,2,\ldots . \]
It is always assumed that the initial vector x₀ is given.
  1. Borisenko, A.I., Tarapov, I.E., Vector and Tensor Analysis with Applications, Translated by R. Silverman. Dover Publications. Available at: https://www.perlego.com/book/110945/vector-and-tensor-analysis-with-applications-pdf (Accessed: 14 October 2022).
  2. Lay, D.C., Lay, S.R., McDonald, J.J., Linear Algebra and its Applications, Pearson,