Symmetrizable generalized inverses of symmetrizable matrices

John Z. Hearon
1967 Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics  
The matrix A is said to be symmetri zable by V when V is positive definit e and AV is he rmitian. Several le mmas re gard ing symm e trizab ility are given. For three classes of ge neralized inverses it is s hown that if A is s mmetrizable by V the re exists a ge nerali zed inverse in eac h class whi ch is sy mmetrizabl e by V. Th e Moore·Penrose inve rse (or pse udo-inverse) of a matrix sy mm e triza bl e by V is also symmetrizable by V if a nd only if th e matrix and the pseudo-inverse com
more » ... eudo-inverse com mute. Key Word s: Ge neraIized inverse, sy mm etrizable matrix.
doi:10.6028/jres.071b.031 fatcat:2bpmt5i2hnafjp22kuzdyukbfi