Introduction to Matrix

A matrix is a 2-dimensional array, which is a structured collection of numbers arranged in rows and columns. It is rectangular in form, providing a systematic way to organize and navigate through the data. For instance, a matrix  can be represented as:

A = [1,2,3

4,5,6

7,8,9]

Where each number is an element identified by its positional coordinates, designated by its row and column.

Matrix Representation

A matrix is most commonly represented as a two-dimensional array in programming. Essentially, this means that a matrix is depicted as an array of arrays, where each sub-array represents a row containing multiple column elements. Thus, the primary array holds all the rows, making it possible to visualize the data in a grid-like structure reminiscent of a mathematical matrix.

For example, the above mentioned matrix is representation in Python as:

Accessing and Modifying Matrix Elements

In programming, elements of a matrix are accessed using their row and column indices. For instance, to access the element 5 in the matrix A mentioned above, one would reference its position using A[1][1], considering a zero-based index system prevalent in most programming languages. Similarly, modifications to elements are performed by assigning a new value using the respective indices.

Example in Python:

Let's solve some coding problems to see matrix data structure in action.