Search results
Results from the WOW.Com Content Network
Since the identity matrix is also centrosymmetric, it follows that the set of n × n centrosymmetric matrices over F forms a subalgebra of the associative algebra of all n × n matrices. If A is a centrosymmetric matrix with an m -dimensional eigenbasis , then its m eigenvectors can each be chosen so that they satisfy either x = J x or x = − ...
Benzene is a centrosymmetric molecule having a centre of symmetry at the centre. In crystallography, a centrosymmetric point group contains an inversion center as one of its symmetry elements. [1] In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z).
Bisymmetric matrices are both symmetric centrosymmetric and symmetric persymmetric.; The product of two bisymmetric matrices is a centrosymmetric matrix. Real-valued bisymmetric matrices are precisely those symmetric matrices whose eigenvalues remain the same aside from possible sign changes following pre- or post-multiplication by the exchange matrix.
An "almost" triangular matrix, for example, an upper Hessenberg matrix has zero entries below the first subdiagonal. Hollow matrix: A square matrix whose main diagonal comprises only zero elements. Integer matrix: A matrix whose entries are all integers. Logical matrix: A matrix with all entries either 0 or 1.
An exchange matrix is the simplest anti-diagonal matrix. Any matrix A satisfying the condition AJ = JA is said to be centrosymmetric. Any matrix A satisfying the condition AJ = JA T is said to be persymmetric. Symmetric matrices A that satisfy the condition AJ = JA are called bisymmetric matrices. Bisymmetric matrices are both centrosymmetric ...
If the matrix is symmetric indefinite, it may be still decomposed as = where is a permutation matrix (arising from the need to pivot), a lower unit triangular matrix, and is a direct sum of symmetric and blocks, which is called Bunch–Kaufman decomposition [6]
The wurtzite structure is non-centrosymmetric (i.e., lacks inversion symmetry). Due to this, wurtzite crystals can (and generally do) have properties such as piezoelectricity and pyroelectricity, which centrosymmetric crystals lack. [citation needed]
An Toeplitz matrix may be defined as a matrix where , =, for constants , …,. The set of n × n {\displaystyle n\times n} Toeplitz matrices is a subspace of the vector space of n × n {\displaystyle n\times n} matrices (under matrix addition and scalar multiplication).