ABSTRACT
The introduction of matrices enables to write many formulae more compactly and in a more suggestive way. This chapter introduces the basic rules of calculating with matrices. If the entries of the matrix have definite numerical values, the matrix must be written out in full. A matrix equation between m × n matrices is equivalent to mn scalar equations. For matrices there is a further important operation: the multiplication of matrices. The behaviour of the zero matrix resembles that of the scalar zero under multiplication as well as addition. Block decomposition is often helpful in carrying out the multiplication of matrices with many entries. An extreme case of a rectangular matrix is a vector: a column vector of dimension n may be considered as an n × 1 matrix, and from this point of view the way in which a matrix operates on a column vector is just an instance of matrix multiplication.
