A skew-symmetric function, also known as an antisymmetric function, is a function ( f ) that satisfies the property ( f(x, y) = -f(y, x) ) for all ( x ) and ( y ) in its domain. This means that swapping the inputs results in the negation of the function's value. Skew-symmetric functions are often encountered in fields like linear algebra and physics, particularly in the context of determinants and cross products. An example is the function ( f(x, y) = x - y ).
x=y²
A Bessel function is any of a class of functions which are solutions to a particular form of differential equation and are typically used to describe waves in a cylindrically symmetric system.
Symmetric
yes, it is both symmetric as well as skew symmetric
An even function is symmetric about the y-axis. If a function is symmetric about the origin, it is odd.
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
Odd Function
The only function that can be symmetric about the x-axis is the x-axis itself. For each value of x a function, f(x), can have at most one value for f(x). Otherwise it is a mapping or relationship but not a function.
For lithium with identical electrons, the ground state wave function is a symmetric combination of the individual electron wave functions. This means that the overall wave function is symmetric under exchange of the two identical electrons. This symmetric combination arises from the requirement that the total wave function must be antisymmetric due to the Pauli exclusion principle.
It means that the probability density function is symmetric about 0.
x=y²
f(x) = 0 is a constant function. This particular constant function is both even and odd. Requirements for an even function: f(x) = f(-x) Geometrically, the graph of an even function is symmetric with respect to the y-axis The graph of a constant function is a horizontal line and will be symmetric with respect to the y-axis. y=0 or f(x)=0 is a constant function which is symmetric with respect to the y-axis. Requirements for an odd function: -f(x) = f(-x) Geometrically, it is symmetric about the origin. While the constant function f(x)=0 is symmetric about the origin, constant function such as y=1 is not. and if we look at -f(x)=f(-x) for 1, we have -f(x)=-1 but f(-1)=1 since it is a constant function so y=1 is a constant function but not odd. So f(x)=c is odd if and only iff c=0 f(x)=0 is the only function which is both even and odd.
if it is symmetric and centered at the origin, It is can be called an odd function
symmetric about the y-axis symmetric about the x-axis symmetric about the line y=x symmetric about the line y+x=0
A Bessel function is any of a class of functions which are solutions to a particular form of differential equation and are typically used to describe waves in a cylindrically symmetric system.
If the function, or channel, or whatever you are reffering to has a axis of symmetry across both the y-axis and the x-axis