This is a new paperback edition of probably the most important and widely read text on numerical analysis. It is the distillation of what the author learnt about the computation of matrix eigenvalues by dint of trying all methods known to him on computers he helped to make. He was establishing the special nature of these computations as he wrote, and this, along with his emphasis on understanding rather than proving theorems, resulted in an informal and very readable work which became an almost instant classic.