Theory of Matrices
Sam Perlis
Addison- Wesley
The  main theme of the book is  the  establishment  of  the well-
known canonical  forms.  Rank, nonsingularity, and inverses  are
introduced in connection with  the  development of canonical matrices
under  the  relation of equivalence, and without  the  intervention
of determinants. Congruence  and  Hermitian congruence are  the
next  major  topics.