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A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

A mathematical object is said to be symmetric if it is invariant ("looks the same") under a symmetry transformation. A function, matrix, etc., is symmetric if it remains ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

Any square matrix A can be written as a sum A=A_S+A_A, (1) where A_S=1/2(A+A^(T)) (2) is a symmetric matrix known as the symmetric part of A and A_A=1/2(A-A^(T)) (3) is an ...

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...

The symmetric successive overrelaxation (SSOR) method combines two successive overrelaxation method (SOR) sweeps together in such a way that the resulting iteration matrix is ...

An asymmetric matrix is a square matrix that is not symmetric, i.e., a matrix A such that A^(T)!=A, where A^(T) denotes the transpose. An asymmetric matrix therefore ...

An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...

A square matrix is called bisymmetric if it is both centrosymmetric and either symmetric or antisymmetric (Muir 1960, p. 19).