What is Inverse?

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What is Inverse?
Inverse is a computer program which aims at finding solutions to a wide range of inverse and optimization problems which arise in different environments. Inverse provides solutions to the problems which involve complex numerical simulations. Most of these problems arise during a scientific enquiry. Solution to problems is found out with a set of algorithm.

Inverse problems develop during the process of scientific inquiry or when technology is developed. These problems will be connected with an analysis programme. Inverse problems arise when a mathematical topic and environmental problem is co-related. They find applications in medical imaging, location of a mineral or oil deposit on the surface of the earth, optimization of shapes, life science modelling, finding cracks in the interior of a material etc.

Inverse functions are defined in mathematics. A function is denoted as f and its inverse as f-1.Inverse of a function can be found out easily by graphical method. Inverse functions find applications in calculus, trigonometry and set theory. Inverses can be partial or complete.

Inverse does not exist for all matrices. Inverse exists for a square matrix whose determinant is not zero. The product of a square matrix and its inverse gives an identity matrix as the result. When a matrix has an inverse it is said to be invertible or non-singular. There are several methods for inverting a matrix such as Gauss Jordan elimination and LU decomposition.

The inverse of a trigonometric function in mathematics is known as cyclometric function. Inverse is defined for algebraic values. The most commonly used trigonometric functions are sin-1 x, cos-1 x and tan-1x.

Inverse square law is defined in physics. The physical law relates strength and distance. According to the law physical strength and square of the distance will be in inverse proportions. The law holds when force or energy is radiated outwards from a point source. Gravitation and electrostatics justifies the law.

Inverse variation is defined in algebra. The value of two variables changes in opposite manner. When the value of one variable increases the other is subjected to a decrease. Inverse variations can be found in many of the real world examples.

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