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Encapsulation in the mechanism that binds together code and data and that leaps both safe from outside interference or misuse. It also allows the creation of an object. More simply, an object in a logical entity that encapsulate both data and the code that manipulators that data. Within an object, some of the code and/ or data may be private to the objected and in accessible to anything outside the object. In this way and object provides a significant level of protection against some other unrelated part of the program accidentally modifying or incorrectly using the private parts of the object.

The wrapping up of data and functions into a single unit (called class) is known as encapsulation. Data encapsulation is the most striking feature of a class. The data is not accessible to the outside world and only those functions which are wrapped in the class can access it. These functions provide the interface between the object’s data and the program. This insulation of the data from direct access by the program is called ‘ data hiding ‘. Abstraction refers to the act of representing essential features without including the background details or explanations. Classes use the concept of abstraction and are defined as a list of abstract attributes such as size, weight and cost, and functions to operate on these attributes. They encapsulate al1 the essential properties of the objects that are to be created. Since the classes use the concept of data abstraction, they are known as Abstract Data Types (ADT).

This tutorial discusses some of the ins and outs of matrices. Matrices can be fun, but more importantly, they can really save you time.  Introduction A matrix is, by definition, a rectangular array of numeric or algebraic quantities which are subject to mathematical operations. Matrices can be defined in terms of their dimensions (number of rows and columns). Let us take a look at a matrix with 4 rows and 3 columns (we denote it as a 4×3 matrix and call it  A ): Each individual item in a matrix is called a cell, and can be denoted by the particular row and column it resides in. For instance, in matrix A, element a32 can be found where the 3rd row and the 2nd column intersect. What are they used for? Matrices are used to represent complicated or time-consuming mathematical operations. A single matrix can hold an infinite number of calculations, which can then be applied to a number, vector, or another matrix. There are several operations that can be done on matrices, inc