Introduction to Matrix

This post is about some basic introduction to matrix.

Matrices are everywhere. If you have used a spreadsheet program such as MS Excel, or Lotus, written a table (such as in Ms-Word), or even have used mathematical or statistical software such as Mathematica, Matlab, Minitab, SAS, SPSS, Eviews, etc., you have used a matrix. Let us start with the Introduction to matrix.

Introduction to Matrix

Matrices make the presentation of numbers clearer and make calculations easier to program. For example, the matrix is given below about the sale of tires in a particular store given by quarter and make of tires.

FirestoneQ1Q2Q3Q4
Tirestone212032
Michigan5111524
Copper614728

It is called a matrix, as information is stored in a particular order and different computations can also be performed. For example, if you want to know how many Michigan tires were sold in Quarter 3, you can go along the row ‘Michigan’ and column ‘Q3’ and find that it is 15.

Similarly, the total number of sales of ‘Michigan’ tiers can also be found by adding all the elements from Q1 to Q4 in the Michigan row. It sums to 55. So, a matrix is a rectangular array of elements. The elements of a matrix can be symbolic expressions or numbers. Matrix $[A]$ is denoted by;

Introduction to Matrix

Row $i$ of the matrix $[A]$ has $n$ elements and is $[a_{i1}, a_{i2}, \cdots, a_{1n}] and column of $[A]$ has $m$ elements and is $\begin{bmatrix}a_{1j}\\ a_{2j} \\ \vdots\\ a_{mj}\end{bmatrix}$.

The size (order) of any matrix is defined by the number of rows and columns in the matrix. If a matrix $[A]$ has $m$ rows and $n$ columns, the size of the matrix is denoted by $(m\times n)$. The matrix $[A]$ can also be denoted by $[A]_{m\times n}$ to show that $[A]$ is a matrix that has $m$ rows and $n$ columns in it.

Each entry in the matrix is called the element or entry of the matrix and is denoted by $a_{ij}$, where $i$ represents the row number and $j$ is the column number of the matrix element.

Matrix of tire Sale

The above-arranged information about sales and types of tires can be denoted by the matrix $[A]$, that is, This matrix has 3 rows and 4 columns. So, the order (size) of the matrix is 3 x 4. Note that element $a_{23}$ indicates the sales of tires in ‘Michigan’ in quarter 3 (Q3). That is all about Introduction to Matrix.

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