American Mathematical Monthly Problem 11415
نویسنده
چکیده
Definitions. a) A matrix is called a complex matrix if all its entries are complex numbers. (In particular, any vector in C is considered a n× 1 complex matrix.) b) For any complex matrix A, we denote the matrix A T by A∗. c) Let U2 (C) be the group of all unitary 2× 2 complex matrices. In other words, let U2 (C) = { U ∈ GL2 (C) | U∗ = U−1 } . d) A complex matrix A is called Hermitian if it satisfies A∗ = A. Problem. Let A1, A2, ..., An be n Hermitian 2 × 2 complex matrices. Define a function F from the Cartesian product (U2 (C)) to R by
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