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A strictly upper triangular matrix is an upper triangular matrix having 0s along the diagonal as well as the lower portion, i.e., a matrix A=[a_(ij)] such that a_(ij)=0 for ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

Householder (1953) first considered the matrix that now bears his name in the first couple of pages of his book. A Householder matrix for a real vector v can be implemented ...

Given a reference triangle DeltaABC, the trilinear vertex matrix of another triangle DeltaA^'B^'C^' is the 3×3 matrix whose rows are the trilinear coordinates of the vertices ...

Two points z and z^S in C^* are symmetric with respect to a circle or straight line L if all circles and straight lines passing through z and z^S are orthogonal to L. Möbius ...

A matrix whose elements may contain complex numbers. The matrix product of two 2×2 complex matrices is given by (1) where R_(11) = ...

The set of elements belonging to one but not both of two given sets. It is therefore the union of the complement of A with respect to B and B with respect to A, and ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

B(x,y)=[x y; +/-ty +/-x]. (1) It satisfies B(x_1,y_1)B(x_2,y_2)=B(x_1x_2+/-ty_1y_2,x_1y_2+/-y_1x_2). (2) Powers of the matrix are defined by B^n = [x y; ty x]^n (3) = [x_n ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...