Computational methods of linear algebra:
V. N. Faddeeva · 1952
The siM of the linear transformations A and B will be a transformation C which associates the vector X with the vector AX + BX» This sum of linear transformations is obviously itself a linear transformation.2 e Representation of a linear transforation by a matrix .Let us choose, in the space R , some basis e^, e-1} ee * , © r .A linear transformation relates to the vectors of the basis the vectors Ae" , Ae~, *»» , Ae 8 Let Ae ... ( , °• e, Ae be given in terms of their coordinates with respect to the basis e^, e 0 , e^, i,e 6 , let