Examples of using Diagonal elements in English and their translations into Russian
{-}
-
Official
-
Colloquial
The diagonal elements of the covariance matrix are real.
Trace of square matrix is the sum of diagonal elements of this matrix.
The sum of the diagonal elements of a matrix is called the trace of the matrix.
In the second option define number of diagonal elements other than zero.
The diagonal elements(M) of the Hamiltonian are due to strong interaction physics which conserves strangeness.
We draw cards' sketches in the style of website- with various diagonal elements.
For network quality assessment diagonal elements(their maximum and minimum) inverse weight matrix are also used.
One can choose andaxis in such way that effective permittivity will be described by tensor with 3 nonzero diagonal elements, and.
Square grids in each layer of chords can be reinforced with diagonal elements that are not directly connected to the webs.
The two diagonal elements must be equal, since the particle and antiparticle have equal masses in the absence of the weak interactions.
These formulas consist of two relations infinite Toeplitz determinants, the diagonal elements of which are the coefficients of algebraic equations.
All diagonal elements M i i{\displaystyle M_{ii}} in a tuned filter are equal to zero because a susceptance vanishes at the resonant frequency.
From this it is easily seen that all three matrices have determinant 1,as the determinant of a triangular matrix is simply the product of its diagonal elements, which are all 1 for both Ln and Un.
Reasonable structure with diagonal elements and tension rod at the bottom allow carrying weight of the big tabletop made of oak veneered plywood.
Undulating elements and different types of loops(vertical, horizontal, connective loops)as well as saber diagonal elements produced a major impact on the graphic of writing.
Because the eigenvalues of a triangular matrix are its diagonal elements, for general matrices there is no finite method like gaussian elimination to convert a matrix to triangular form while preserving eigenvalues.
When such triangular factors are nonsingular, it is useful, before solving the linear system, to transform them the product ofa diagonal matrix and a triangular matrix whose diagonal elements are equal to 1.
In the complex QZ decomposition, the ratios of the diagonal elements of S to the corresponding diagonal elements of T, λ i S i i/ T i i{\displaystyle\lambda_{ i}= S_{ ii}/ T_{ ii}}, are the generalized eigenvalues that solve the generalized eigenvalue problem A v λ B v{\displaystyle Av=\lambda Bv} where λ{\displaystyle\lambda} is an unknown scalar and v is an unknown nonzero vector.
The linear number of the parallel form layers consisting of a single division slows the performance of the parallel version and is a bottleneck of the algorithm, especially compared to the forward substitution,where the diagonal elements are equal to 1.
But this is equal to⟨ ψ| x, x⟩+⟨ ψ| x, y⟩+⟨ ψ| y, x⟩+⟨ ψ| y, y⟩{\displaystyle\langle\psi|x, x\rangle+\langle\psi|x, y\rangle+\langle\psi|y, x\rangle+\langle\psi|y,y\rangle\,} The first and last terms on the right hand side are diagonal elements and are zero, and the whole sum is equal to zero.
If the above approaches do not lead to a sufficient accuracy of the Cholesky decomposition, then the Ajiz-Jennings approach can be used to modify the main diagonal of a matrix: if a small element[ math]\ ell_{ ij}[/ math] should be dropped,then its absolute value is added to the diagonal elements[ math]\ ell_{ ii}[/ math] and[ math]\ ell_{ jj}/ math.
It is interesting to note that the original Cholesky decomposition is available in the largest western libraries, whereas the faster[math]LU[/math] decomposition algorithm without square-root operations is used only in special cases(for example, for tridiagonal matrices)when the number of diagonal elements is comparable with the number of off-diagonal elements. .
As a rule,a correction refers to the diagonal element in the output table.
Each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
A graph contains a triangle if and only if the cube of its adjacency matrix contains a nonzero diagonal element, so finding a triangle may be performed in the same asymptotic time bound as n× n matrix multiplication.
Every its off-diagonal element M i j{\displaystyle M_{ij}} is the coupling coefficient of ith and jth resonators k i j.{\displaystyle k_{ij}.}Every diagonal element M i i{\displaystyle M_{ii}} is the normalized susceptance of the ith resonator.
The values of elements diminish toward zero away from the diagonal, where all elements have value 1.
All these elements can be vertical, diagonal, or curved.
The model of a single multilevel one-electron atom with violated symmetry such that its transition dipole-moment operator has constant diagonal matrix elements, among which not all are pairwise equal to each other, has been studied.
It has also been demonstrated that a two-level quantum system,whose transition dipole operator has constant unequal diagonal matrix elements, can continuously fluoresce under excitation with monochromatic laser radiation at a much lower frequency than the frequency of the exciting radiation.