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The regularity of a linear combination of r consecutive elements of a monic d-orthogonal polynomial sequence has been studied when (r−1) is a multiple of d. This problem can be solved without the introduction of the concept of d-quasi-orthogonality. In the present contribution, we deal with the problem of d-orthogonality of a linear combination of two elements of a monic d-orthogonal polynomial sequence. This problem is also equivalent to the study the regularity of the left product of a linear form by a matrix polynomial of degree one.
d-orthogonal polynomials; d-dimensional vectors of linear forms; recurrence relations; linear combinations of d-orthogonal polynomials; chebyshev d-orthogonal polynomials; associated and co-recursive d-orthogonal polynomials