Some Complete Calculi for Matrices
A matrix calculus is introduced with the intention of developing data structures
suitable for a high level algorithmic language for mathematical programming.  
The paper investigates how the special structure of matrices can be described
and utilized for efficient computing by saving memory space and
superfluous operations.  Sequences of Matrices (and sequences of sequences
of matrices) are considered, and matrix operators areext
ended to sequence operators and cumulative operators.  Algorithms
are given which use symbol manipulation of matrix expressions so
as to find the forms best suited for computation.  These forms are
called normal forms.  Several completeness results are obtained
in the sense that for each expression an equivalent expression
in normal form can be found within a specified calculus.
CACM April, 1970
Bayer, R.
Witzgall, C.
