In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Example: The following 3∗3 matrix is symmetric: 1. Basic Properties The sum and difference of two symmetric matrices is again symmetric. This is not always true for the product: given symme...
Properties: Any matrix A can be written as a sum of /symmetric matrix and a skew-symmetric matrix. A=12(A+A′)+12(A−A′) Questions to solve Question 1: Check whether the given matrices are symmetric or not. M = [0590] P = [140−1] Solution: We will first find the transp...
symmetric-silimar-symmetric matrixThis paper generalizes (anti)symmetric matrices, (anti) bisymmetric matrices and D-(anti) symmetric matrices, defines the symmetric-silimar-(anti)symmetric matrix and study its properties.Minghui WangQiaohua Liu
Symmetric Matrices: A square matrix {eq}A {/eq} is said to be symmetric if {eq}\displaystyle A^T = A {/eq}. Properties of symmetric matrix: If... Learn more about this topic: Matrix Definition & Examples from Chapter 4/ Lesson 2 ...
2.2 Some definitions and properties The matrix A is symmetric when AT = A, where T means transpose, i.e. when Aij = Aji for all i, j. Otherwise A is unsymmetric. A symmetric matrix A is said to be positive definite when (2.6)yTAy > 0 for any vector y having at least one ...
The generalized hypergeometric function with m x m complex symmetric matrices X and Y is defined by Properties of matrix variate confluent hypergeometric function distribution Semidefinite Programming (SDP) is a type of optimisation in which one minimises linear objective function subject to the constraint...
A few properties related to symmetry in matrices are of interest to point out: 1. The product of any (not necessarily symmetric) matrix and its transpose is symmetric; that is, both AA′ and A′A are symmetric matrices. 2. If A is any square (not necessarily symmetric) matrix, then A...
In this paper, we consider the matrix representations of the finite field, and show some conclusions of the primitive matrix representation of the finite field on the ground field by using the properties of the cyclotomic polynomial. We obtain the symmetric matrix representation of the finite field...
5)real anti-sub-symmetric matrix实反次对称矩阵 1.The paper discusses sub-diagonal andreal anti-sub-symmetric matrix,and gives several properties of these two kinds of special matrix.针对次对角矩阵与实反次对称矩阵进行了讨论,给出了次对角矩阵的特征值、实反次对称矩阵的次特征值及次特征向量等的性质...
Determinant preserving maps on 2×2 and 3×3symmetric matrixspaces; 三元域上2×2和3×3阶对称矩阵空间保行列式的映射 2. The unique of inverse eigenvalue problem for asymmetric matrix; 一个对称矩阵特征值反问题的唯一性 3. Various properties ofsymmetric matrixand anti-symmetric matrix; ...