matrix groupsLet G be a group, an automorphism phi : G -> G is called a commuting automorphism, if for all x is an element of G, phi(x)x = x phi(x). Let U-n (F) be the group consisting of all n x n unit upper triangular matrices over a field F with characteristic char(...
Each of the four matrices in this formula is either an upper-triangular or a lower-triangular Toeplitz matrix that is generated by either a vector u or a vector v. In the case of the ICZT, a symmetric Toeplitz matrix needs to be inverted. This leads to a simplified formula that ...
An element stiffness matrix and a material's stiffness matrix in each lattice segment are assigned effective properties, based on a number of presented fibers by each element. They can then be calculated in unit cells of a lattice network, i.e., triangular, square, hexagonal lattice units; ...
Thus, the key to the ICZT algorithm is finding a computationally efficient way to invert this Toeplitz matrix. The Gohberg–Semencul formula23,24 expresses the inverse of a Toeplitz matrix as a difference between two products of upper-triangular and lower-triangular Toeplitz matrices. These four ...
We can use the observation matrix and the Potter [22] algorithm to solve the decoupling matrix. They suggest that the decoupling matrix V should be the upper triangular matrix that has the right diagonal elements and that its orthogonalization can fully determine its elements. The details of ...
An n× n matrix is called a square matrix. A matrix with all entries equal to zero is called a zero matrix; it is denoted by 0. A square zero matrix with the elements on the main diagonal, that is, the diagonal extending from the upper left corner to the lower right corner, ...
Vectors are read all at once from the Unified Buffer, but must be fed diagonally into the MM Array. This is accomplished with a set of sequential buffers in a lower triangular configuration. The top valu e reaches the matrix immediately, the second after one cycle, the third after two, et...
Being about PUnit isn't really a topic. Let's follow the existing convention that Foo instances about Bar are in Algebra.Foo.Bar.
paired bones that form the upper, lateral sides of the skull sacrum single triangular bone that is a part of the pelvis and just below the the lumbar vertebrae sagittal suture joint that unites the right and left parietal bones at the midline along the top of the skull ...
The upper triangular part of the matrix represented the correlation coefficients between the factors and the lower triangular part was the variations of correlations between Timin and 13 meteorological variables. The larger red font presented significant correlations. The correlations between Timin and ...