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Collineatory Transformation of a Square Matrix Into Its Transpose
Author(s) -
Foulkes H. O.
Publication year - 1942
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s1-17.2.70
Subject(s) - transpose , transformation (genetics) , square matrix , square (algebra) , mathematics , matrix (chemical analysis) , physics , geometry , materials science , chemistry , symmetric matrix , composite material , biochemistry , eigenvalues and eigenvectors , quantum mechanics , gene
In this paper some general results on certain matrices derived from the general linear associative algebra are stated. These are used in the special case of a polynomial algebra to obtain matrix solutions H , of order n , of the equation HA = A'H , where A is any square matrix [ a ij ] of the same order. The solutions are given explicitly for n = 2 and n = 3, and their construction for higher values of n is indicated. The results can be applied directly to numerical cases, and, when H is non‐singular * , give collineatory transformations of A into its transpose. Various linear relations between the solutions obtained by this method are discussed fully for n = 2 and 3.