for problem (a), all real numbers of value r will make the system linearly independent, as the system contains more vectors than entry simply by insepection. As for problem (b), no value of r can make the system linearly dependent by insepection. I tried reducing the matrix into reduced...
For the definition given by least squares approximation, the error function r (x) is smooth in [a, b] continuous derivative y (x) are linearly independent; least squares approximation can be obtained by solving the following matrix k times iterative solution: ...
We show that the diagonalizer of the exact GJBD problem can be given by $W=[x_1, x_2, \\dots, x_n]\\Pi$, where $\\Pi$ is a permutation matrix, $x_i$'s are eigenvectors of the matrix polynomial $P(\\lambda)=\\sum_{i=0}^p\\lambda^i A_i$, satisfying that $[x_1,...
The function ψ 0 and a set of model functions n are used to construct a set, ψ n = ψ 0 n, of linearly independent correlated basis functions... HW Jackson,E Feenberg - 《Annals of Physics》 被引量: 94发表: 1961年 Linearly dependent subspaces and the eigenvalue spectrum of the one...
If P is not invertible, the matrix A is not diagonalizable, or equivalently, A does not have enough linearly independent eigenvectors that would form a basis. L = diagonal(A) n = size(A, 1) [P , D] = eig(A); // I must find the number of k linearly independen...
inearly independent Find all markers in the genotype matrix that are linearly independentFind all markers in the genotype matrix that are linearly independentgeno.matrix
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Summary: In this paper, we consider the exact/approximate general joint block diagonalization (GJBD) problem of a matrix set {Ai}i=0p ( p ≥ 1), where a nonsingular matrix W (often referred to as a diagonalizer) needs to be found such that the matrices W HAiW 's are all ...
In this paper, we consider the exact/approximate general joint block diagonalization (GJBD) problem of a matrix set { A i } i = 0 p ( p ≥1), where a nonsingular matrix W (often referred to as a diagonalizer) needs to be found such that the matrices W H A i W 's are all ...
The density matrix was computed from the density using basis orbitals which form linearly independent products (LIP). Calculations were performed on the Be atom using LIP bases containing several of the natural spin orbitals from an accurate nonrelativistic 650-term configuration interaction (CI) ...