Matrix Representation
James E. H. Davidson · 2018
Cells of a matrix contain numbers, represented in mathematical manipulations by a single symbol. Vectors and matrices provide the notation needed to compactly represent systems of linear equations. In the context of matrix algebra, ordinary numbers are known as scalars since they possess scale but no dimension. Matrix multiplication is a fundamental operation defined for pairs of matrices satisfying certain conformability conditions, although these are different from the conditions for a sum. Matrix algebra satisfies the associative rule. It is often convenient to break a matrix into blocks of rows, or blocks of columns, to distinguish different components of an expression or to ease certain calculations. The most important aspect of partitioning is its treatment in algebraic manipulations. When adding or multiplying partitioned matrices, the rules can be applied almost as if the blocks were just scalar elements.