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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).
A matrix whose elements are of the form 1/(x i + y j) for (x i), (y j) injective sequences (i.e., taking every value only once). Centrosymmetric matrix: A matrix symmetric about its center; i.e., a ij = a n−i+1,n−j+1. Circulant matrix: A matrix where each row is a circular shift of its predecessor. Conference matrix
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]
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.
Cabibbo–Kobayashi–Maskawa matrix; Cartan matrix; Cauchy matrix; Centering matrix; Central groupoid; Centrosymmetric matrix; Circulant matrix; Column groups and row groups; Community matrix; Commutation matrix; Companion matrix; Comparison matrix; Completely-S matrix; Complex Hadamard matrix; Compound matrix; Condition number; Conductance ...
A matrix equation of the form = is called a Toeplitz system if is a Toeplitz matrix. If is an Toeplitz matrix, then the system has at most only unique values, rather than . We might therefore expect that the solution of a Toeplitz system would be easier, and indeed that is the case.