My purpose in wrlting this book is to bring to the attention of tlw reader, some
recent developments in the field of Matrix. Calculus. Although some concepts,
such as Kronecker matrix. products, the vector derivative etc. are mentioned in
a few specialised books, no book, to my knowledge, is totally devoted to this
subject. The interested researcher must consult numerous published papers to
appreciate the scope of the concepts involved.
Matrix. calculus applicable to square matrices was developed by Turnbull
[29,30] as far back as 1927. The theory presented in this book is based on the
works of Dwyer and McPhail [15] published in 1948 and others mentioned in
the Bibliography. It is more general than Turnbull's development and is applicable
to non·square matrices. But even this more general theory has grave limitationS,
in particular it reqUires that in general the matrix elements are non constant and
independent. A symmetric matrix, for example, is treated as a special case.
Methods of overcoming some of these limitations have been suggested, but I am
not aware of any published theory wllich is both quite general and simple enough
to be useful.