Symmetric Property

Symmetric property is the one of the main property of those properties which has mathematics. It will occur in all kinds of mathematics. The property says that even though the occurrence of some transformations something does not change. In a transformation if one object is obtained from other than the two objects are said to be symmetric to one another. Symmetric property is an equivalence relation.  Symmetric Property in Geometry and Matrix:  Symmetric property of Geometry:  Symmetry is very much helpful in graphing an equation. Here if we know one part of the graph then we will also get the symmetric portion of the graph.  In matrix:  A square matrix A = [aij] is said to be symmetric if for all i and j.  Example:  (a) y = x^2 - 6 x^4 + 2  Symmetry about the x-axis:  Here, we need to replace the entire 'y' with '-y'.  Hence, this is not an equivalent equation. Therefore, this equation does not have symmetry about theEigen values and eigenvectors are real of a symmetric matrix.  The eigenvector of a symmetric matrix are orthogonal  Symmteric Property in Algebra:  Symmetric Property of Equality  The following property  If u1 = v1 then v1 = u1.  In algebra, we can found the symmetry of an expression by the following steps  Symmetry about x-axis:  Symmetry about y-axis:  Symmetry about origin: x-axis.  Symmetry about the y-axis:  Here replace all 'x' with '-x'.  ' y = (-x)^2 - 6 (-x)^4 + 2  y = x^2 - 6x^4 + 2  The result shows that both are equivalent. Therefore, this equation does have the symmetry about the y-axis.  Symmetry about the origin:  Here we replace both variables with '-x', '-y'.  -y = (-x)^2-6(-x)^4+2  -y = x^2-6x^4+2  Therefore, this is not equivalent to the original equation and we do not have the symmetry about the origin.