Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: inverse matrix

Bottom of Page

1 to 6 of 6

  1.  
    • 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

1 to 6 of 6

  1.