Matrix is a set of numbers arranged in rows and columns to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics. Just like we perform Addition and Subtraction on numbers, it is possible to add or subtract two matrices provided they have the same number of rows and columns.
Operations on Matrices:
Addition of matrices
To add matrices X and Y, add the elements of X to the corresponding elements of Y.
For example, the element in the first row and the first column of matrix X is added to the element in the first row and the first column of matrix Y. Similarly, the other corresponding elements are added.
Matrix addition can be performed only over matrices with the same order.
Subtraction of matrices
Matrices can also be subtracted in a manner to the addition operation. That is, the elements of one matrix are subtracted from the corresponding elements of the other matrix. Again, matrix subtraction can be performed only over matrices with the same order.
Multiplication of matrices (Dot Product)
Matrix multiplication is a binary operation that produces a matrix from two matrices. The definition is motivated by linear equations and linear transformations on vectors, which have numerous applications in applied mathematics, physics, and engineering. If A is an n × m matrix and B is an m × p matrix, their matrix product AB is an n × p matrix, in which the m entries across a row of A are multiplied with the m entries down a column of B and summed to produce an entry of AB.
- Each number or entity in a matrix is called its element
- In a matrix, the horizontal lines are called rows; whereas the vertical lines are called columns
- Matrices, in general, are denoted by capital letters, say A