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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 16th 2024

    added references listing formulas for inverses of various block matrices

    diff, v8, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2024
    • (edited May 19th 2024)

    Urs, I’d like to pay your attention that these are quasi-research papers without any serious contribution to the subject nor giving the balanced view of the area. Besides (for the second paper) MDPI Mathematics is a predatory journal without really rigorous refereeing. I recently got a paper in integral equations to referee (!), which I rejected to do, being clearly incompetent in the subject.

    Inverses of block matrices are written at many places for at least about 150 years (since Cayley and Silvester) and their modern formulation is the Gel’fand-Retakh theory of quasideterminants from 1990-1991. The formulas for block matrices were often taught in engineering courses in 20th century (more than to mathematicians). (P.S. I have thought them myself as an example to non-math students including last year for school teachers).

    Quasideterminant is an entry (at a transposed place) of an inverse of the matrix with noncommutative entries, for example a block matrix or even a matrix of morphisms in a suitable Abelian category; the subject deals with a plethora of formulas and rules for those entries.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2024

    Add a reference, if you have one at hand!

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2024

    For example,

    • D. Krob, B. Leclerc, Minor identities for quasi-determinants and quantum determinants, Comm. Math. Phys. 169 (1995) 1–23 doi arXiv:hep-th/9411194

    discusses inverses of block matrices and motivating quasideterminants in Sec. 2 (the work is expanding on Gelfand-Retakh work).

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2024

    Added idea section.

    diff, v10, current

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeMay 19th 2024

    Added a section on variants.

    diff, v10, current