let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

The space l^p with 1≤p∞ is the set of real numbers that satisfy _(n=1)^∞▒〖|x_n |^p∞〗.The function in vector X which has value fulfills norm-2 properties denoted by ,⋅‖ and pair (X,‖⋅,⋅‖) called space.A said to be complete or a Banach-2 if every Cauchy sequence converges an element space.This research was conducted prove norm-2.The first step completeness norm contained satisfies norm-2.Next, de...

The paper examines relationships between the Shannon entropy and the `α-norm for n-ary probability vectors, n ≥ 2. More precisely, we investigate the tight bounds of the `α-norm with a fixed Shannon entropy, and vice versa. As applications of the results, we derive the tight bounds between the Shannon entropy and several information measures which are determined by the `α-norm. Moreover, we app...