anticommuting algebradecomposition of rotationmatrix solutionnonlinear Klein–Gordon equationnonlinear wave equationunitary anti-Hermitian matrixWe improve the construction of exact matrix solutions for nonlinear wave equations by using unitary anti-Hermitian and anticommuting matrices. We prove the theorem that...
摘要: Let Dq(n) be the quantized matrix algebra introduced by Dipper and Donkin. It is shown explicitly that the defining relations of Dq(n) form a Grbner-Shirshov basis. Consequently, several structural properties of Dq(n) are derived....
is equal to the product of the diagonal entries of because is upper triangular. How to citePlease cite as:Taboga, Marco (2021). "Properties of the determinant", Lectures on matrix algebra. https://www.statlect.com/matrix-algebra/determinant-properties.The...
Find the eigenvalues of SolutionHow to citePlease cite as:Taboga, Marco (2021). "Properties of eigenvalues and eigenvectors", Lectures on matrix algebra. https://www.statlect.com/matrix-algebra/properties-of-eigenvalues-and-eigenvectors.The books Most of the learning materials found on this web...
We study a class of matrices with noncommutative entries, which were first considered by Yu.I. Manin in 1988 in relation with quantum group theory. They are defined as “noncommutative endomorphisms” of a polynomial algebra. More explicitly their defining conditions read: (1) elements in the ...
Explore the determinant of a matrix, which is widely used in linear algebra. Understand how to find the determinant of a matrix with determinant rules and learn to determine the order of the matrix.Updated: 11/21/2023 Determinant of a Matrix ...
Perturbations on the subdiagonals of Toeplitz matrices Let L be an Hermitian linear functional defined on the linear space of Laurent polynomials. It is very well known that the Gram matrix of the associated bi... K Castillo,L Garza,F Marcellán - 《Linear Algebra & Its Applications》 被引...
In particular, if A is an M-matrix of order n, we obtain the inequality q( A A 1)1 n. M Fiedler,TL Markham - 《Linear Algebra & Its Applications》 被引量: 169发表: 1988年 The Hadamard Operator Norm Of A Circulant And Applications Let Mn be the space of n x n complex matrices...
(≥2)an integer,I_v the identity matrix of order v,and J_v the all-one matrix of order v.Let={aI_v+βJ_u,∈GL_u(F)|a,β∈F},and={C∈GL_v(F)|the row-sums and the column-sums of C are all equal}.In this paper,we study (1) the center and the centralizer of ,(2...
Discover what a singular matrix is and what it means. Learn about the properties of a singular matrix. Using examples, learn what makes a matrix...