Introduction to matrices

• The word 'matrices' is derived from the Latin word 'matrix' which means 'mother'.
• The word 'matrices' is plural of the word 'matrix'
• The term matrix was first introduced by the mathematician Arther Cayley in 1860
• Matrices are used to represent systems of linear equations, data analysis, computer graphics, cryptography etc.
• Each element of a matrix is called its entry
• A matrix with m rows and n columns is said to be an mxn matrix or a matrix of size mxn
• If all entries of a matrix are complex numbers then it is called a complex matrix
• If all entries of a matrix are real numbers then it is called a real matrix
• An empty matrix has no elements at all
• A column vector is a matrix with only one column
• A row vector is a matrix with only one row
• In general we use uppercase letters (e.g., A) to denote matrices and lower case letters (e.g., x) to denote column vectors
• The transpose of a matrix A, denoted by AT, is the matrix obtained from A by interchanging its rows and columns.
• Matrix is a collection of elements arranged in rows and columns
• A matrix is an array or rectangular table consisting of numbers, symbols or expressions arranged in rows and columns.
• To add two matrices, they must have the same dimensions (same number of rows and columns). The sum of corresponding entries is computed and placed into the resulting matrix.
• Matrices are used to represent systems of linear equations, data analysis, optimization problems, and many other applications.
• Subtraction of matrices follows similar rules as addition, but involves subtracting instead of adding.
• The rows of a matrix run horizontally
• The columns of a matrix run vertically