Contribution to the study on Con Secondary k Normal Bimatrices

Abstract

The present thesis consisting of six chapters is primarily confined to a study newlineon Con. Secondary k-normal bimatrices. newlineIn chapter I, Review of literature, notations, basic definitions preliminary newlineresults and summary of results obtained in this thesis are given. newlineIn chapter II, The Secondary k-normal and con. secondary k- normal newline(Conjugate Secondary k-Normal) bimatrix is defined and its characterizations are newlineobtained and also the equivalent condition of Con. Secondary k-normal bimatrices are newlinediscussed. newlineIn chapter III, The properties of con. secondary k-normal bimatrices are newlinediscussed. The sum of secondary k-normal bimatrices in n n R and#61620; and con. Secondary newlinek-normal bimatrices in n n C and#61620; are derived. newlineIn chapter IV, Con. Secondary k-normal bimatrix Solutions to the Toeplitz newlinematrices. Con. secondary k-normal circulant bimatrices, con. secondary k-normal newlinecentrosymmetric and centrohermitian bimatrices are also discussed. newlineIn chapter V, The inequalities on con. secondary k-normal bimatrices are newlineobtained. star partial ordering of conjugate secondary k-normal bimatrices and minus newlinepartial ordering of conjugate secondary k-normal bimatrices are discussed. The newlineSeveral characterizations for B B A Band#61482; and#61603; and B B A B and#61485; and#61603; in the case of conjugate newlinesecondary k-normal bimatrices are determined. newlineIn chapter VI, The generalized inverses of con. secondary k-normal bimatrices newlineare discussed. The secondary k-generalized inverse exists for particular kind of square