Two important examples of linear transformations are the zero transformation and the identity transformation. We obtain a set of linear equations, whose solution is found at the cost of an n × n matrix inversion (remember that n is the dimension of the configuration space, it is small in general). If a generating function is unique, the investment does not have a single solution and the number of solutions characterizes the caustic one. In mathematics, an identity function, also called identity relationship, identity map, or identity transformation, is a function that always returns the value that was used as an argument, unchanged.

Let g be a rotation of the plane R2, different from the identity transformation of R2 and from all the central symmetries of R2. This definition is generalized to the concept of identity morphism in category theory, where M endomorphisms need not be functions. When the function is evaluated on a given input, the corresponding output is calculated according to the order of the operations. Formally, if M is a set, the identity function f in M is defined as a satisfactory function with M as the domain and codomain. The identity function in M is clearly an injective function and a subjective function, so it is bijective.

Therefore, the periodic L-F transformation 2T is first used to transform the equation (into a vector field in which the linear part is invariant in time). The special transformations lambda that can be reached continuously from the identity transformation of M, n constitute the special pseudo-orthogonal group SO (m, n), called the group of pseudo-signature rotations (m, n). In particular, IdM is the identity element of the monoid of all functions from M to M (in composition of functions). In other words, when f is the identity function, the equality f (X) %3D X is true for all the values of X to which f can be applied.

For example, the following matrix equation is another way of writing the identity transformation equations X′%3Dx, Y′%3Dy. The following video example describes another linear transformation of identity and its corresponding graphic.

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