314K pdf
... respectively, for x = (x1 , . . . , xn ) ∈ Rn . Let L(Rn ; Rm ) be the set of linear maps from Rn to Rm , which we identify with the set of m × n matrices in the usual way. If A ∈ L(Rn ; Rm ) and if p, q ∈ {1, 2, ∞} then the norm of A induced by the p-norm on Rn and the q-norm on Rm is kAkp,q = sup{ ...
... respectively, for x = (x1 , . . . , xn ) ∈ Rn . Let L(Rn ; Rm ) be the set of linear maps from Rn to Rm , which we identify with the set of m × n matrices in the usual way. If A ∈ L(Rn ; Rm ) and if p, q ∈ {1, 2, ∞} then the norm of A induced by the p-norm on Rn and the q-norm on Rm is kAkp,q = sup{ ...
