Matriitsed

Matriitsed are a fundamental concept in linear algebra, representing rectangular arrays of numbers, symbols, or expressions arranged in rows and columns. These arrays are enclosed in brackets or parentheses and are commonly used to represent systems of linear equations, transformations, and data sets. The dimensions of a matrix are denoted by the number of rows and the number of columns, for example, an m x n matrix has m rows and n columns.

Basic operations can be performed on matrices, including addition, subtraction, and multiplication. Matrix addition and subtraction are performed element-wise, meaning corresponding elements of the matrices are added or subtracted, provided the matrices have the same dimensions. Matrix multiplication, however, is more complex and follows specific rules involving the dot product of rows and columns.

Matrices have numerous applications across various fields. In computer graphics, they are used to perform transformations such as translation, rotation, and scaling of objects. In physics, matrices represent linear operators and are used in quantum mechanics and classical mechanics. In economics, they model input-output relationships and solve systems of linear equations representing economic interactions. Data science and machine learning extensively utilize matrices for storing and manipulating large datasets and for implementing algorithms like regression and neural networks. The study of matrices and their properties is a core component of advanced mathematics.