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Square matrix
About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.
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TL;DR: In this paper, a necessary and sufficient condition for a 3 × 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries is presented, and an algorithm for testing the unitary equivalence of such a matrix can be found.
32 citations
TL;DR: In this paper, the determinant of the distance matrix of a tree with n vertices is defined in a natural way, which involves only the determinants of the sum and the product of the weight matrices of the tree.
32 citations
TL;DR: In this article, the matrix elements of the U(n) generators in the electronic Gel'fand basis were derived and a general matrix element formula was derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods.
Abstract: This is the first paper in a series of three directed toward the evaluation of spin-dependent Hamiltonians directly in the spin-orbit basis. In this paper we present a new and complete derivation of the matrix elements of the U(n) generators in the electronic Gel'fand basis. The approach employed differs from previous treatments in that the matrix elements of nonelementary generators are obtained directly. A general matrix element formula is derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods. A simple relationship between the matrix elements of raising and lowering generators is determined which indicates that in CI calculations, only the matrix elements of raising generators need be calculated. Some results on the matrix elements of products of two generators are also presented.
32 citations
TL;DR: In this article, the authors developed a new inversion-free method for obtaining the minimal Hermitian positive definite solution of the matrix rational equation X + A ∗ X - 1 A = I, where I is the identity matrix and A is a given nonsingular matrix.
32 citations
Patent•
02 Sep 1998TL;DR: A PET decoder for an ATM network has a modular architecture including a processing unit having various memories and a processing pipeline for constructing from a block of m data of a certain number of bits, a square matrix A based on a vector D of relative points over the Galois field as mentioned in this paper.
Abstract: A PET decoder for an ATM network has a modular architecture including a processing unit having various memories and a processing pipeline for constructing from a block of m data of a certain number of bits, a square matrix A based on a vector D of relative points over the Galois field. The processing pipeline also decomposes by triangular factorization the square matrix A and solves the subsystem of equations by simple substitution. The decoder also includes a control unit interfacing with the ATM network, a programmable parallel processor, a random access memory and the processing unit.
32 citations