Linear maps preserving numerical radius of tensor products of matrices V članku so karakterizirane linearne preslikave na tenzorskem produktu kompleksnih matrik, ki ohranjajo numerični radij. Let ▫\$m,n ge 2\$▫ be positive integers. Denote by ▫\$M_m\$▫ the set of ▫\$m times m\$▫ complex matrices and by ▫\$w(X)\$▫ the numerical radius of a square matrix ▫\$X\$▫. Motivated by the study of operations on bipartite systems of quantum states, we show that a linear map ▫\$phi colon M_{mn} to M_{mn}\$▫ satisfies ▫\$\$w(phi(Aotimes B)) = w(A otimes B)quad text{for all } A in M_m text{ and } B in M_n\$\$▫ if and only if there is a unitary matrix ▫\$U in M_{mn}\$▫ and a complex unit ▫\$xi\$▫ such that ▫\$\$phi(A otimes B) = xi U(varphi_1(A) otimes varphi_2(B))U^ast quad text{for all } A in M_m text{ and } B in M_n\$\$▫ where ▫\$varphi_k\$▫ is the identity map or the transposition map ▫\$X mapsto X_t\$▫ for ▫\$k = 1,2\$▫, and the maps ▫\$varphi_1\$▫ and ▫\$varphi_2\$▫ will be of the same type if ▫\$m,n ge 3\$▫. In particular, if ▫\$m,n ge 3\$▫, the map corresponds to an evolution of a closed quantum system (under a fixed unitary operator), possibly followed by a transposition. The results are extended to multipartite systems. 2013 2013-10-15 12:04:32 1033 matematika, teorija matrik, kompleksne matrike, linearni ohranjevalci, numerični rang, numerični radij, tenzorski produkt, mathematics, matrix theory, complex matrices, linear preservers, numerical range, numerical radius, tensor product, r6 Ajda Fošner 70 Zejun Huang 70 Chi-Kwong Li 70 Nung-Sing Sze 70 ISSN 2 0022-247X UDK 4 512.643 COBISS_ID 3 16648025 0 Predstavitvena datoteka 2013-10-15 12:04:32