Matrix (mathematics)
Definition and Overview
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The numbers, symbols, or expressions are referred to as the elements or entries of the matrix. Matrices have wide applications in engineering, physics, applied mathematics, and statistics.
History
The concept of a matrix was first introduced by the English mathematician James Sylvester in 1850. However, the term "matrix" was coined by another English mathematician, Arthur Cayley, in 1858.
Types of Matrices
There are various types of matrices, each with unique properties and applications.
Scalar Matrix
A scalar matrix is a type of matrix in which all the elements of the principal diagonal are equal, and all other elements are zero.
Diagonal Matrix
A diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
Identity Matrix
An identity matrix, also known as a unit matrix, is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros.
Zero Matrix
A zero matrix is a matrix in which all the elements are zero.
Row Matrix
A row matrix is a matrix that has only one row.
Column Matrix
A column matrix is a matrix that has only one column.
Square Matrix
A square matrix is a matrix in which the number of rows is equal to the number of columns.
Rectangular Matrix
A rectangular matrix is a matrix in which the number of rows is not equal to the number of columns.
Matrix Operations
There are several operations that can be performed on matrices, including addition, subtraction, multiplication, and division.
Matrix Addition
Matrix addition is the operation of adding two matrices by adding the corresponding entries together.
Matrix Subtraction
Matrix subtraction is the operation of subtracting one matrix from another by subtracting the corresponding entries.
Matrix Multiplication
Matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix.
Matrix Division
Matrix division, also known as matrix inversion, is the process of finding a matrix that, when multiplied with the original matrix, gives an identity matrix.
Applications of Matrices
Matrices are used in various fields such as physics, computer graphics, statistics, and probability theory. They are also used in practical applications such as the representation of data, solving systems of equations, and signal processing.
