Geodesic
A class of optimally conditioned block $2\times2$ matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 64-76 
L. Yu. Kolotilina. A class of optimally conditioned block $2\times2$ matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 64-76. http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a4/
@article{ZNSL_2002_284_a4,
     author = {L. Yu. Kolotilina},
     title = {A class of optimally conditioned block $2\times2$ matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--76},
     year = {2002},
     volume = {284},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A block $2\times2$ Hermitian positive-definite (h.p.d.) matrix is called equilibrated if its diagonal blocks coincide with the corresponding blocks of its inverse. It is demonstrated that any block $2\times2$ h.p.d. matrix is block diagonally similar to an equilibrated matrix, and any equilibrated matrix is optimally conditioned. Other properties of equilibrated matrices are also established.