The rank of a matrix is equal to the number of linearly independent columns in the matrix. This means that the rank can be used to determine if the columns of a matrix are linearly independent. If the rank is equal to the number of columns, then the columns are linearly independent.Simil...
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) wavefu...
When it is more, the solution currents at different locations are not line-arly independent, meaning that the obtained neural currents are mathematically, rather than physiologically, determined by the beamformer weight matrices or the MNLS pseudoin-verse matrix, which should be avoided for further...
inearly independent Find all markers in the genotype matrix that are linearly independentFind all markers in the genotype matrix that are linearly independentgeno.matrix
In this case, (6) is a system of p linearly independent equations. Using the notation H, defined in (5) for scalar sequences, the difference equation (6) can be written as a matrix equation [R0R1⋯Rn]D=0,whereD=Hℓ+1,T−ℓ(w).Note that, in this case, the data matrix...
For the definition of the minimum 2 times closer, if error function R(x) in the [A, B] of continuous smooth can be imported, and the y (x) Linear independent multiplied by 2 and the smallest can be resolved by the following matrix approach of K iterations: ...
Solving General Joint Block Diagonalization Problem via Linearly Independent Eigenvectors of a Matrix Polynomialgeneral joint block diagonalizationmatrix polynomialtensor decompositionIn this paper, we consider the exact/approximate general joint block diagonalization (GJBD) problem of a matrix set $\\{A_i...
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) ...
When it is more, the solution currents at different locations are not linearly independent, meaning that the obtained neural currents are mathematically, rather than physiologically, determined by the beamformer weight matrices or the MNLS pseudoinverse matrix, which should be avoided for further ...
We show that the diagonalizer of the exact GJBD problem can be given by W = [x(1),x(2), horizontal ellipsis ,x(n)]pi, where pi is a permutation matrix and x(i)'s are eigenvectors of the matrix polynomial P(lambda)= n-ary sumation i=0p lambda iAi, satisfying that [x(1),...