Thus the scattering matrix can be described and parametrized in terms of the symmetric part of the T-matrix, instead of a potential function. The off-diagonal elements of the symmetric part are arbitrary except for a weak condition imposed on them by the range of the force, while the ...
Therefore, the Hessian is always a symmetric matrix. It plays a prominent role in the sufficiency conditions for optimality as discussed later in this chapter. It will be written as (4.5)H[∂2f∂xj∂xi];i=1 to n,j=1 to n The gradient and Hessian of a function are calculat...
The necessary and sufficient conditions for the existence of and the expressions for the symmetric solutions of matrix equations (I) AX + YA = C , (II) AXA T + BYB T = C , and (III) ( A T XA , B T XB ) = ( C, D ) are derived. In addition, the minimum-2-norm least-...
Let A be a skew-symmetric matrix. Then by definition A'=-Athe (i, j)th element of A' = the (i, j)th element of(- A)→the (j,i)th element of A= -the (i, j)th element of AFor the diagonal elements i= j二the (i,i)th element of A=- -the (i,i)th elementthe (i...
The symmetric Toeplitz matrix \(\widehat{{\boldsymbol{W}}}\) can be inverted10 using a special case of the Gohberg–Semencul formula23,24. In other words, the inverse matrix \({{\boldsymbol{{\hat{W}}}^{-1}\) is given by: $${{\boldsymbol{{\hat{W}}}^{-1}=\frac{1}{{...
samples from either a light-tailed (finite variance) or heavy-tailed distribution in the domain of attraction of a symmetric $\alpha$-stable distribution, where $\alpha\in(0,2]$ may depend on the layer. For the bias terms of the layer, we assume i.i.d. initializations with a symmetric...
If rank distance of a code is equal to d, than a code can correct not only all the errors of rank up to ⌊(d-1)/2⌋ but also many symmetric errors of rank beyond this bound. 3. Matrix representations of finite fields Let(3.2)g0=(g1,g2,…,gn),gj∈Fqn,be a basis of Fqn...
One-mode proximity data are defined between the objects from a single set and are usually given in the form of a square symmetric matrix; two-mode proximity data are defined between the objects from two distinct sets and are given in the form of a rectangular matrix. In addition, there is...
A square matrix is called skew-symmetric if AT =- A.39. Prove that the main diagonal of a skew-symmetric ma-trix must consist entirely of zeros. 相关知识点: 试题来源: 解析 答案:见解析 解析:令ai为反对称矩阵的主对角元 则a=-a 故aii=0 知识点:矩阵的运算 ...
Define Symmetric (matrix). Symmetric (matrix) synonyms, Symmetric (matrix) pronunciation, Symmetric (matrix) translation, English dictionary definition of Symmetric (matrix). n. Mathematics A matrix that is its own transpose. American Heritage® Dictio