Inverses of quasi-tridiagonal matrices
Copyright policy )Inverses of quasi-tridiagonal matrices
A blockmatrix \(T=[T_{ij}]\) with square blocks \(T_{ii}\) is quasi- triangular, if \(T_{ij}=0\) for \(| i-j|>1\). Explicit formulas for the inverses of quasi-triangular matrices are given. The inverses can be characterized by the quasi-triangle property: \(R=[R_{ij}]\) has the q.t.p. if all \(R_{ii}\) nonsingular and \(R_{ij}=R_{ik}R^{- 1}_{kk}R_{kj}\) for all \(ik>j\). Theorem 3: Let K be a nonsingular block matrix whose diagonal blocks \(K_{ii} (i=2,...,n- 1)\) are nonsingular. Then K has the q.t.p. iff its inverse is quasi- tridiagonal.
- University of Lucknow India
Numerical Analysis, blockmatrix, Algebra and Number Theory, quasi triangular, inverses, Explicit formulas for the inverses, Discrete Mathematics and Combinatorics, quasi-triangle property, Theory of matrix inversion and generalized inverses, Geometry and Topology
Numerical Analysis, blockmatrix, Algebra and Number Theory, quasi triangular, inverses, Explicit formulas for the inverses, Discrete Mathematics and Combinatorics, quasi-triangle property, Theory of matrix inversion and generalized inverses, Geometry and Topology
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