Matrix is a way of storing data, especially numbers in a rectangular array, arranged in rows and columns format. Each data (number) in a matrix is called its element or entry. Every matrices are denoted by a capital letter.
Introduction to Matrix
Storing data and keeping records in real life is essential. We might store them in different forms.
Matrix is the way of storing data, especially numbers in rectangular arrays, arranged in rows and columns format. Each data (number) in a matrix is called its element or entry.
The plural of matrix is matrices.
Notation of Matrices
Here are the important things to remember during the notation of Matrices:
Matrices are always denoted by capital letters.
Elements or entries of any matrix are denoted by small letters. The letter should be the same used to denote the respective matrix.
The elements are further denoted by double suffix format, based on their position in the matrix.
EXAMPLE: How to denote the elements of a matrix?
$\text{A} = \left [ \displaylines{1 & 2 & 3 \\ 4 & 5 & 6} \right ]_{2\text{x}3}$
In the above example, the matrix is denoted by the capital letter 'A'. So, we call the matrix A.
Now, we need to note the elements of this matrix. For this, we will first use the same letter we used to denote the matrix i.e. 'A'. We know that elements of the matrix are denoted by small letters. So, it will be 'a'. Also, they are denoted by double suffixes. The suffixes are written by analyzing the rows and columns. In the suffix, the first number denotes rows and the second number denotes the column.
GOOD TO KNOW
Rows are the horizontal lines whereas columns are the vertical lines.
In the above matrix, to notate element 3, we would write 'a12'. This is because element 3 lies on the first row and second column. For 4, 'a22'. Similarly, to denote 6, we would write 'a23' and so on.
Let us notate the above matrix 'A'. Here is the answer:
$\text{A} = \left [ \displaylines{a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23}} \right ]_{2\text{x}3}$
Order or Size of the Matrix
While writing the order or size of the matrix, we write the total number of rows and columns in suffixes. While the matrix is denoted by the Capital letter. Writing the order of the above matrix would be A2x3.
So, things to remember:
Use the same capital letter that you used to denote the matrix.
Count the total number of rows and columns. Then, write them in a suffix with 'x' (by sign) in the middle.
Rows (also denoted by i) are written before the 'x' sign and columns (also denoted by j) are written after the 'x' sign.
Some people may be confused with the notation of the elements matrix and the order of the matrix because they are pretty much the same. Remember, in the notation of elements of a matrix, small letters are used. In order of matrix, capital letters are used with a 'x' sign in between the two suffixes.
That is:
$A_{1 \times 1}$ represents a matrix A having 1 row and 1 column.
$a_{11}$ represents an element of matrix A whose location is in the 1st row and the 1st column.