Geodesic
A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application
Glasgow mathematical journal, Tome 11 (1970) no. 1, pp. 81-83

Voir la notice de l'article provenant de la source Cambridge University Press

We denote by F the field R of real numbers, the field C of complex numbers, or the skew field H of real quaternions, and by Fn an n dimensional left vector space over F. If A is a matrix with elements in F, we denote by A* its conjugate transpose. In all three cases of F, an n × n matrix A is said to be hermitian if A = A*, and we say that two n × n hermitian matrices A and B with elements in F can be diagonalized simultaneously if there exists a non singular matrix U with elements in F such that UAU* and UBU* are diagonal matrices. We shall regard a vector u ∈ Fn as a l × n matrix and identify a 1 × 1 matrix with its single element, and we shall denote by diag {A1, ..., Am} a diagonal block matrix with the square matrices A1, ..., Am lying on its diagonal. 
Au-Yeung, Yik-Hoi. A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application. Glasgow mathematical journal, Tome 11 (1970) no. 1, pp. 81-83. doi: 10.1017/S0017089500000859
@article{10_1017_S0017089500000859,
     author = {Au-Yeung, Yik-Hoi},
     title = {A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application},
     journal = {Glasgow mathematical journal},
     pages = {81--83},
     year = {1970},
     volume = {11},
     number = {1},
     doi = {10.1017/S0017089500000859},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000859/}
}
TY  - JOUR
AU  - Au-Yeung, Yik-Hoi
TI  - A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application
JO  - Glasgow mathematical journal
PY  - 1970
SP  - 81
EP  - 83
VL  - 11
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000859/
DO  - 10.1017/S0017089500000859
ID  - 10_1017_S0017089500000859
ER  - 
%0 Journal Article
%A Au-Yeung, Yik-Hoi
%T A necessary and sufficient condition for simultaneous diagonalization of two hermitian matrices and its application
%J Glasgow mathematical journal
%D 1970
%P 81-83
%V 11
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000859/
%R 10.1017/S0017089500000859
%F 10_1017_S0017089500000859

[1] 1.Radon, J., Lineare Scharen orthogonaler Matrizen, Abh. Math. Sem. Univ. Hamburg 1 (1922), 1–14. Google Scholar | DOI

[2] 2.Lee, H. C., Eigenvalues and canonical forms of matrices with quaternion coefficients, Proc. Roy. Irish Acad. Sect. A 52 (1949), 253–260. Google Scholar

[3] 3.Wonenburger, M. J., Simultaneous diagonalization of symmetric bilinear forms, J. Math. Mech. 15 (1966), 617–622. Google Scholar

Cité par Sources :