Introduction and dimension of a matrix

Introduction and dimension of a matrix

Introduction to Matrices

What is a Matrix?

• A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
• The numbers, symbols or expressions inside the matrix are called its elements or entries.
• Matrices are used to solve a variety of mathematical problems, including systems of linear equations and transformations in geometry.

Basic Terms

• The rows of a matrix run horizontally while the columns run vertically.
• The entry or number in the i-th row and j-th column of a matrix is usually denoted by a_ij.

Dimensions of a Matrix

Definition

• The dimension of a matrix refers to the number of rows and columns it has.
• Dimensions are written as “rows x columns”. For example, a matrix with 2 rows and 3 columns is a 2x3 matrix (read as “two by three”).

Matrix Types by Dimension

• A matrix with the same number of rows and columns is called a square matrix.
• A row matrix or row vector has only one row but can have multiple columns.
• A column matrix or column vector has only one column but can have multiple rows.
• The zero matrix or null matrix has all its entries equal to zero.

Important Note

• Be aware that order matters when identifying a matrix by its dimension. A 2x3 matrix is not the same as a 3x2 matrix.