Matrix

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. It's a fundamental concept in mathematics, physics, computer science, and various other fields. Matrices are used to represent linear transformations, solve systems of equations, and organize data. A matrix is often denoted by capital letters and elements within the matrix are identified by their row and column indices. Operations such as addition, subtraction, and multiplication are defined for matrices, enabling complex calculations and data manipulation. The size of a matrix, referred to by its number of rows and columns, determines the feasibility of specific operations.

Matrix meaning with examples

• In linear algebra, a 2x2 matrix can represent a rotation or scaling of a 2D vector space. For instance, a rotation matrix would involve trigonometric functions to transform a vector's coordinates. This allows for operations like rotating an image or calculating its new location. Matrices also facilitate solving systems of linear equations, representing multiple constraints.
• In computer graphics, matrices are essential for transforming 3D objects. A model's vertices can be represented as a matrix and then transformed by a series of matrices, each accounting for translation, rotation, and scaling. This enables realistic rendering and animation, shaping virtual worlds from simple geometries into complex scenes, making game development dynamic.
• A social network can be modeled as a matrix, where rows and columns represent users, and cell values indicate connections or relationships. Analyzing this matrix can reveal key individuals or groups within the network and aid in community detection, or the spread of information. Using a matrix represents data sets and the relationships between different entities.
• In economics, an input-output matrix captures the flow of goods and services between different sectors of the economy. This matrix is used to analyze interdependencies and to estimate the impact of changes in one sector on the others. This allows economists to gauge the broader impacts of changes in supply and demand in the economy.