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Introduction to Matrix

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by

Atith Adhikari
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Matrix is a way of storing data, especially numbers in 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 array, 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 notation of Matrices:

  • Matrices are always denoted by capital letter.
  • Elements or entries of any matrix are denoted by small letter. The letter should be the same used to denoted the respective matrix.
  • The elements are further denoted by double suffix format, on the basis of 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 a capital letter ‘A’. So, we call the matrix as matrix A.

Now, we need to notate the elements of this matrix. For this, we will first use the same letter we used to denoted 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 suffix. The suffix are written by analysing the rows and columns. In the suffix, first number denotes rows and the second number denotes the column.

GOOD TO KNOW

Rows are the horizontal lines where columns are the vertical lines.

In the above matrix, to notate element 3, we would write ‘a12‘. This is because the element 3 lies on the first row and second column. For 4, ‘a22‘. Similarly, to denoted 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 suffix. While, the matrix is denoted by the Capital letter. Writing the order of the above matrix would be A2×3.

So, things to remember:

  • Use the same capital letter that you used to denoted the matrix.
  • Count the total number of rows and columns. Then, write them in 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 notation of elements matrix and order of the matrix because they are pretty much the same. Remember, in notation of elements of matrix, small letters are used. In order of matrix, capital letters are used with a ‘x’ sign in between of the two suffix.

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.