The sequence / structure alignment and DD matrix analysis information is then fed into a modified quaternion eigenvalue algorithm to rapidly perform the structural superposition and calculate the RMSD between aligned regions of two macromolecules.
12.
Gene Golub served as the president of the Society for Industrial and Applied Mathematics ( SIAM ) from 1985 to 1987 and was founding editor of both the SIAM Journal on Scientific Computing ( SISC ) and the SIAM Journal on Matrix Analysis and Applications ( SIMAX ).
13.
Martin founded Martin Analysis Software Technology Company following retirement; and contracted with the Navy for high-resolution beamforming with generalized eigenvector / eigenvalue ( GEVEV ) digital signal processing from 1985 through 1987 and for personal computer aided engineering ( PC CAE ) of underwater transducers and arrays from 1986 through 1989 . Martin published an expanded theory of matrices in 2012 entitled " A New Approach to Matrix Analysis, Complex Symmetric Matrices, and Physically Realizable Systems ".
14.
Regrettably, to confuse the matter, some literature sources use the reverse notation, e . g ., \ succ is replaced with \ prec, most notably, in Horn and Johnson, " Matrix analysis " ( Cambridge Univ . Press, 1985 ), Definition 4.3 . 24, while the same authors switch to the traditional notation, introduced here, later in their " Topics in Matrix Analysis " ( 1994 ), and in the second edition of " Matrix analysis " ( 2013 ).
15.
Regrettably, to confuse the matter, some literature sources use the reverse notation, e . g ., \ succ is replaced with \ prec, most notably, in Horn and Johnson, " Matrix analysis " ( Cambridge Univ . Press, 1985 ), Definition 4.3 . 24, while the same authors switch to the traditional notation, introduced here, later in their " Topics in Matrix Analysis " ( 1994 ), and in the second edition of " Matrix analysis " ( 2013 ).
16.
Regrettably, to confuse the matter, some literature sources use the reverse notation, e . g ., \ succ is replaced with \ prec, most notably, in Horn and Johnson, " Matrix analysis " ( Cambridge Univ . Press, 1985 ), Definition 4.3 . 24, while the same authors switch to the traditional notation, introduced here, later in their " Topics in Matrix Analysis " ( 1994 ), and in the second edition of " Matrix analysis " ( 2013 ).
