value that depends solely on the matrix entries, and that is related to some of the matrix algebraic properties. For example, and most importantly, a matrix is invertible if and only if its determinant is non-zero. We can only compute determinants of square matrices of the form NxN - this...
xj − yj The determinant of (θi,j)1≤i,j≤n is called the Bezoutian. Note that our definition of Bezoutians is different from the Bezoutians defined in =-=[1,2]-=-, which is defined for n non-homogeneous polynomials in n − 1 variables, and is in the ideal generated by ...
of convergence of the joint moments, which depend on two parameters s and h, of the characteristic polynomial of a random Haar-distributed unitary matrix and its derivative, as the matrix size goes to infinity, has been studied for two decades, beginning with the thesis of Hughes (On the ...
(15) Evaluating the eigenvalues eigenvalues (i = 1, 2, … m) of matrix Bm by solving determinant equation of det|Bm − tEm| = 0, we obtain the ti = 2(1 + b) − 2b cosθi, where θi = (2i − 1)π/(2m + 1). Next, constructing the matrix transform by the following...
= ddx1ddx2 vol(SO(d + 1, 1)) φ(x1)φ(x2) φ(x1)φ(x2) = 1 2dvol(SO(1, 1)) × vol(SO(d)) φ(0)φ(∞) φ(0)φ(∞) , (C.1) where vol(SO(1, 1)) × vol(SO(d)) is the stabilizer group for two points and the factor 2d is the Fadeev-Popov determinant. ...
Based on the conception of the matrix volume,we presented the definition of the orthogonal degree of the matrices,generalized and extended the determinant method mentioned above. 基于矩阵体积的概念,引入矩阵向量正交度,对病态问题的行列式诊断方法进行了推广和扩展。 更多例句>> 补充...